Details of a Researcher - HONDA Atsufumi

本稿では，3次元ド・ジッター空間S³₁の空間的平均曲率1曲面に現れる非退化な特異点に対し，それらの分類および非退化特異点の間の双対性を紹介する．本稿の内容は，佐藤媛美氏との共同研究[A. Honda and H. Sato, Singularities of spacelike mean curvature one surfaces in de Sitter space, preprint (arXiv:2103.13849)]に基づく．

On the existence of four or more curved foldings with common creases and crease patterns

Honda A., Naokawa K., Saji K., Umehara M., Yamada K.

BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY 2021.10 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Publisher：Springer Joint Work

Geometry of lightlike locus on mixed type surfaces in Lorentz-Minkowski 3-space from a contact viewpoint

Atsufumi Honda, Shyuichi Izumiya, Kentaro Saji, Keisuke Teramoto

Tsukuba Journal of Mathematics 45 ( 1 ) 51 - 68 2021.7 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Joint Work

Other Link： https://projecteuclid.org/journals/tsukuba-journal-of-mathematics/volume-45/issue-1/Geometry-of-lightlike-locus-on-mixed-type-surfaces-in-Lorentz/10.21099/tkbjm/20214501051.short

Bernstein-Type Theorem for Zero Mean Curvature Hypersurfaces Without Time-like Points in Lorentz-Minkowski Space

Akamine S., Honda A., Umehara M., Yamada K.

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY 52 ( 1 ) 175 - 181 2021.3 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Joint Work

Isometric deformations of wave fronts at non-degenerate singular points

Honda Atsufumi, Naokawa Kosuke, Umehara Masaaki, Yamada Kotaro

HIROSHIMA MATHEMATICAL JOURNAL 50 ( 3 ) 269 - 312 2020.11 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Joint Work

Heinz-type mean curvature estimates in Lorentz-Minkowski space

Honda Atsufumi, Kawakami Yu, Koiso Miyuki, Tori Syunsuke

REVISTA MATEMATICA COMPLUTENSE 34 ( 3 ) 641 - 651 2020.10 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Publisher：Springer Joint Work

Curved foldings with common creases and crease patterns

Atsufumi Honda, Kosuke Naokawa, Kentaro Saji, Masaaki Umehara, Kotaro Yamada

Advances in applied mathematics 121 102083-1 - 102083-10 2020.10 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Joint Work

Duality on generalized cuspidal edges preserving singular set images and first fundamental forms

Atsufumi Honda, Kosuke Naokawa, Kentaro Saji, Masaaki Umehara, Kotaro Yamada

Journal of Singularities 22 59 - 91 2020.9 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Joint Work

Null hypersurfaces in Lorentzian manifolds with the null energy condition

Akamine Shintaro, Honda Atsufumi, Umehara Masaaki, Yamada Kotaro

JOURNAL OF GEOMETRY AND PHYSICS 155 103751-1 - 103751-6 2020.9 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Joint Work

Cuspidal edges with the same first fundamental forms along a knot

Honda Atsufumi, Naokawa Kosuke, Saji Kentaro, Umehara Masaaki, Yamada Kotaro

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 29 ( 7 ) 2020.6 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Joint Work

Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds

Atsufumi Honda, Kentaro Saji, Keisuke Teramoto

Advances in Mathematics 365 107036-1 - 107036-46 2020.5 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Joint Work

Other Link： https://www.sciencedirect.com/science/article/abs/pii/S000187082030061X?via%3Dihub

梅原雅顕・佐治健太郎・山田光太郎（谷島賢二・山田澄生編）：特異点を持つ曲線と曲面の微分幾何学，現代数学シリーズ，19，丸善出版，2017年，xii+319ページ．

本田淳史

数学 72 ( 2 ) 213 - 217 2020.4

DOI CiNii Research

Language：Japanese Publishing type：Research paper (scientific journal) Publisher：一般社団法人日本数学会 Single Work

Duality of singularities for flat surfaces in Euclidean space

Atsufumi Honda

Journal of Singularities 21 132 - 148 2020.3 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Single Work

Geometric invariants of 5/2-cuspidal edges

Honda Atsufumi, Saji Kentaro

ＫＯＤＡＩ　ＭＡＴＨＥＭＡＴＩＣＡＬ　ＪＯＵＲＮＡＬ 42 ( 3 ) 496 - 525 2019.10 [Reviewed]

DOI

Language：English Publishing type：Research paper (scientific journal) Publisher：国立大学法人東京工業大学理学院数学系 Joint Work

We introduce two invariants called the secondary cuspidal curvature and the bias on 5/2-cuspidal edges, and investigate their basic properties. While the secondary cuspidal curvature is an analog of the cuspidal curvature of (ordinary) cuspidal edges, there are no invariants corresponding to the bias. We prove that the product (called the secondary product curvature) of the secondary cuspidal curvature and the limiting normal curvature is an intrinsic invariant. Using this intrinsicity, we show that any real analytic 5/2-cuspidal edges with non-vanishing limiting normal curvature admit non-trivial isometric deformations, which provides the extrinsicity of various invariants.

Other Link： https://ci.nii.ac.jp/naid/130007742214

Isometric realization of cross caps as formal power series and its applications

Atsufumi Honda, Kosuke Naokawa, Masaaki Umehara, Kotaro Yamada

Hokkaido Mathematical Journal 48 ( 1 ) 1 - 44 2019.2 [Reviewed]

DOI Web of Science arXiv

Language：English Publishing type：Research paper (scientific journal) Publisher：Hokkaido University, Department of Mathematics Joint Work

Other Link： https://projecteuclid.org/euclid.hokmj/1550480642

Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space

Atsufumi Honda, Miyuki Koiso, Kentaro Saji

Hokkaido Mathematical Journal 47 ( 2 ) 245 - 267 2018.6 [Reviewed]

DOI Web of Science arXiv

Language：English Publishing type：Research paper (scientific journal) Publisher：Hokkaido University, Department of Mathematics Joint Work

Fold singular points play important roles in the theory of maximal surfaces. For example, if a maximal surface admits fold singular points, it can be extended to a timelike minimal surface analytically. Moreover, there is a duality between conelike singular points and folds. In this paper, we investigate fold singular points on spacelike surfaces with non-zero constant mean curvature (spacelike CMC surfaces). We prove that spacelike CMC surfaces do not admit fold singular points. Moreover, we show that the singular point set of any conjugate CMC surface of a spacelike Delaunay surface with conelike singular points consists of (2, 5)-cuspidal edges.

Other Link： https://projecteuclid.org/euclid.hokmj/1529308818

Complete flat fronts as hypersurfaces in Euclidean space

Atsufumi HONDA

Proceedings of the Japan Academy, Ser. A, Mathematical Sciences 94 ( 3 ) 25 - 30 2018.2

DOI Web of Science arXiv

Language：English Publishing type：Research paper (scientific journal) Publisher：The Japan Academy Single Work

By Hartman--Nirenberg's theorem, any complete flat hypersurface in Euclidean space must be a cylinder over a plane curve. However, if we admit some singularities, there are many non-trivial examples. Flat fronts are flat hypersurfaces with admissible singularities. Murata--Umehara gave a representation formula for complete flat fronts with non-empty singular set in Euclidean 3-space, and proved the four vertex type theorem. In this paper, we prove that, unlike the case of n=2, there do not exist any complete flat fronts with non-empty singular set in Euclidean (n+1)-space
(n ¥geq 3).

Other Link： https://projecteuclid.org/euclid.pja/1519808414

Duality of singularities for spacelike CMC surfaces

Atsufumi Honda

Kobe Journal of Mathematics 34 ( 1-2 ) 1 - 11 2017.12 [Reviewed]

Language：English Publishing type：Research paper (scientific journal) Publisher：Kobe University Single Work

We prove the duality of singularities for spacelike CMC surfaces
in the Lorentz-Minkowski 3-space.

Other Link： http://www.math.kobe-u.ac.jp/jmsj/kjm/abstracts.html

Isometric immersions with singularities between space forms of the same positive curvature

Atsufumi Honda

Journal of Geometric Analysis 3 ( 27 ) 2400 - 2417 2017.7 [Reviewed]

DOI Web of Science arXiv

Language：English Publishing type：Research paper (scientific journal) Publisher：Springer US Single Work

In this paper, we give a definition of coherent tangent bundles of space form type, which is a generalized notion of space forms. Then, we classify their realizations in the sphere as a wave front, which is a generalization of a theorem of O'Neill and Stiel: any isometric immersion of the n-sphere into the (n+1)-sphere of the same sectional curvature is totally geodesic.

Other Link： https://link.springer.com/article/10.1007%2Fs12220-017-9765-8

Mixed type surfaces with bounded mean curvature in 3-dimensional space-times

Atsufumi Honda, Miyuki Koiso, Masatoshi Kokubu, Masaaki Umehara, Kotaro Yamada

Differential Geometry and its Applications 52 ( 14 ) 64 - 77 2017.6 [Reviewed]

DOI Web of Science arXiv

Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier, Inc. Joint Work

In this paper, we shall prove that space-like surfaces with bounded mean curvature functions in real analytic Lorentzian 3-manifolds can change their causality to time-like surfaces only if the mean curvature functions tend to zero. Moreover, we shall show the existence of such surfaces with non-vanishing mean curvature and investigate their properties.

Other Link： http://www.sciencedirect.com/science/article/pii/S0926224517300360

Minimal Darboux transformations

Udo Hertrich-Jeromin, Atsufumi Honda

Beiträge zur Algebra und Geometrie 58 ( 1 ) 81 - 91 2017.2 [Reviewed]

DOI arXiv

Language：English Publishing type：Research paper (scientific journal) Publisher：Springer Berlin Heidelberg Joint Work

We derive a permutability theorem for the Christoffel, Goursat and Darboux transformations of isothermic surfaces. As a consequence we obtain a simple proof of a relation between Darboux pairs of minimal surfaces in Euclidean space, curved flats in the 2-sphere and flat fronts in hyperbolic space.

Other Link： https://link.springer.com/article/10.1007/s13366-016-0301-y

On associate families of spacelike Delaunay surfaces

Atsufumi Honda

Contemporary Mathematics 675 103 - 120 2016.11 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Publisher：American Mathematical Society Single Work

In a paper of do Carmo and Dajczer, associate families of Delaunay surfaces in the Euclidean 3-space are constructed explicitly and classified completely. Following the method of do Carmo-Dajczer, Sasahara gave a construction of some associate families of spacelike Delaunay surfaces in the Lorentz-Minkowski 3-space. In this paper, we continue the construction and give a complete classification of associate families of spacelike Delaunay surfaces. We also determine their singularity types.

Other Link： http://www.ams.org/books/conm/675/

Weakly complete wave fronts with one principal curvature constant

Atsufumi Honda

Kyushu Journal of Mathematics 70 ( 2 ) 217 - 226 2016.9 [Reviewed]

DOI Web of Science

Language：English Publishing type：Research paper (scientific journal) Publisher：Kyushu University Single Work

Murata and Umehara gave a classification of complete flat fronts in the Euclidean 3-space and proved their orientability. Here, a flat front is a flat surface (i.e., a surface where one of the principal curvatures is identically zero) with admissible singularities. In this paper,we investigate wave fronts where one of the principal curvatures is a non-zero constant. Although they are orientable in the regular surface case, there exist non-orientable examples. We classify weakly complete ones and derive their orientability.

Other Link： https://www.jstage.jst.go.jp/article/kyushujm/70/2/70_217/_article

The lightlike geometry of marginally trapped surfaces in Minkowski space-time

Atsufumi Honda, Shyuichi Izumiya

Journal of Geometry 106 ( 1 ) 185 - 210 2015.4 [Reviewed]

DOI arXiv

Language：English Publishing type：Research paper (scientific journal) Publisher：Springer Basel Joint Work

The lightlike geometry of codimension two spacelike submanifolds in Lorentz-Minkowski space has been developed by Izumiya and Romero Fuster (Selecta Math (N.S.) 13:23-55, 2007) which is a natural Lorentzian analogue of the classical Euclidean differential geometry of hypersurfaces. In this paper we investigate a special class of surfaces (i.e., marginally trapped surfaces) in Minkowski space-time from the view point of the lightlike geometry.

Other Link： https://link.springer.com/article/10.1007/s00022-015-0266-2

Intrinsic properties of surfaces with singularities

Masaru Hasegawa, Atsufumi Honda, Kosuke Naokawa, Kentaro Saji, Masaaki Umehara, Kotaro Yamada

International Journal of Mathematics 26 ( 4 ) 1540008 2015.3 [Reviewed]

DOI Web of Science arXiv

Language：English Publishing type：Research paper (scientific journal) Publisher：World Scientific Publishing Joint Work

In this paper, we give two classes of positive semi-definite metrics on 2-manifolds. The one is called a class of Kossowski metrics and the other is called a class of Whitney metrics: The pull-back metrics of wave fronts which admit only cuspidal edges and swallowtails in R^3 are Kossowski metrics, and the pull-back metrics of surfaces consisting only of cross cap singularities are Whitney metrics. Since the singular sets of Kossowski metrics are the union of regular curves on the domains of definitions, and Whitney metrics admit only isolated singularities, these two classes of metrics are disjoint. In this paper, we give several characterizations of intrinsic invariants of cuspidal edges and cross caps in these classes of metrics. Moreover, we prove Gauss-Bonnet type formulas for Kossowski metrics and for Whitney metrics on compact 2-manifolds.

Other Link： http://www.worldscientific.com/doi/abs/10.1142/S0129167X1540008X

Intrinsic invariants of cross caps

Masaru Hasegawa, Atsufumi Honda, Kosuke Naokawa, Masaaki Umehara, Kotaro Yamada

Selecta Mathematica. New Series 20 ( 3 ) 769 - 785 2014.7 [Reviewed]

DOI Web of Science arXiv

Language：English Publishing type：Research paper (scientific journal) Publisher：Springer Basel Joint Work

It is classically known that generic smooth maps of \R^2 into \R^3 admit only isolated cross cap singularities. This suggests that the class of cross caps might be an important object in differential geometry. We show that the standard cross cap f_{can}(u,v)=(u,uv,v^2) has non-trivial isometric deformations with infinite dimensional freedom. Since there are several geometric invariants for cross caps, the existence of isometric deformations suggests that one can ask which invariants of cross caps are intrinsic. In this paper, we show that there are three fundamental intrinsic invariants for cross caps. The existence of extrinsic invariants is also shown.

Other Link： https://link.springer.com/article/10.1007/s00029-013-0134-6

Transformations and orientability of extrinsically flat surfaces

Atsufumi HONDA

Progress in Surface Theory, Mathematisches Forschungsinstitut Oberwolfach 2013.5

Language：English Publishing type：Research paper (scientific journal) Single Work

Non-convex anisotropic surface energy and zero mean curvature surfaces in the Lorentz-Minkowski space

Atsufumi Honda, Miyuki Koiso, Yasuhiro Tanaka

Journal of Math-for-Industry 5 ( A ) 73 - 82 2013.4 [Reviewed]

Language：English Publishing type：Research paper (scientific journal) Publisher：Kyushu University Joint Work

An anisotropic surface energy functional is the integral of an energy ensity function over a surface. The energy density depends on the surface normal at each point. The usual area functional is a special case of such a functional. We study stationary surfaces of anisotropic surface energies in the euclidean three-space which are called anisotropic minimal surfaces. For any axisymmetric anisotropic surface energy, we show that, a surface is both a minimal surface and an anisotropic minimal surface if and only if it is a right helicoid. We also construct new examples of anisotropic minimal surfaces, which include zero mean curvature surfaces in the three-dimensional Lorentz-Minkowski space as special cases.

Other Link： http://j-mi.org/articles/index/14

Note on the space of oriented geodesics in the three-sphere

Atsufumi Honda

RIMS Ko^kyu^roku Bessatsu B38 169 - 187 2013.4 [Reviewed]

Language：Japanese Publishing type：Research paper (international conference proceedings) Publisher：Kyoto University Single Work

The space of oriented geodesics in the 3-dimensional space form admits a neutral K\"ahler structure naturally. In the case of the Euclidean space, Guilfoyle-Klingenberg investigated the neutral K\"ahler structure, and derived some results which connect the submanifold geometry of the Euclidean space and that of the space of oriented geodesics. Georgiou-Guilfoyle proved similar results in the case of the hyperbolic space. In this note, introducing their results, we show analogue results in the case of the sphere.

Other Link： http://www.kurims.kyoto-u.ac.jp/~kenkyubu/bessatsu.html

Isometric immersions of the hyperbolic plane into the hyperbolic space

Atsufumi Honda

Tohoku Mathematical Journal, Second Series 64 ( 2 ) 171 - 193 2012.6 [Reviewed]

DOI Web of Science arXiv

Language：English Publishing type：Research paper (scientific journal) Publisher：Tohoku University Single Work

In this paper, we parametrize the space of isometric immersions of the hyperbolic plane into the hyperbolic 3-space in terms of null-causal curves in the space of oriented geodesics. Moreover, we characterize "ideal cones" (i.e., cones whose vertices are on the ideal boundary) by behavior of their mean curvature.

Other Link： https://projecteuclid.org/euclid.tmj/1341249370

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Papers - HONDA Atsufumi