HONDA Atsufumi

J-GLOBAL         Last updated: Aug 7, 2019 at 10:57
HONDA Atsufumi
Yokohama National University
Faculty of Engineering Division of Intelligent Systems Engineering
Job title
Associate Professor
Doctor of Science(Tokyo Institute of Technology), Master of Mathematics(Kyushu University)
Research funding number

Research Areas


Academic & Professional Experience

Apr 2017
Associate Professor, Faculty of Engineering Division of Intelligent Systems Engineering, Yokohama National University
Apr 2013
Mar 2017
Lecturer, General Education Division (Sciences), National Institute of Technology, Miyakonojo College


Apr 2010
Mar 2013
Department of Mathematics, Graduate School, Division of Science and Engineering, Tokyo Institute of Technology
Apr 2008
Mar 2010
Department of Mathematics, Graduate School of Mathematics, Kyushu University

Published Papers

Atsufumi Honda, Kosuke Naokawa, Masaaki Umehara, Kotaro Yamada
Hokkaido Mathematical Journal   48(1) 1-44   Feb 2019   [Refereed]
Atsufumi Honda, Miyuki Koiso, Kentaro Saji
Hokkaido Mathematical Journal   47(2) 245-267   Jun 2018   [Refereed]
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 conelik...
Atsufumi Honda
Proceedings of the Japan Academy, Ser. A, Mathematical Sciences   94(3) 25-30   Feb 2018   [Refereed]
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 admissi...
Duality of singularities for spacelike CMC surfaces
Atsufumi Honda
Kobe Journal of Mathematics   34(1-2) 1-11   Dec 2017   [Refereed]
We prove the duality of singularities for spacelike CMC surfaces
in the Lorentz-Minkowski 3-space.
Atsufumi Honda
Journal of Geometric Analysis   3(27) 2400-2417   Jul 2017   [Refereed]
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...
Atsufumi Honda, Miyuki Koiso, Masatoshi Kokubu, Masaaki Umehara, Kotaro Yamada
Differential Geometry and its Applications   52(14) 64-77   Jun 2017   [Refereed]
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 s...
Udo Hertrich-Jeromin, Atsufumi Honda
Beiträge zur Algebra und Geometrie   58(1) 81-91   Feb 2017   [Refereed]
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 i...
Atsufumi Honda
Contemporary Mathematics   675 103-120   Nov 2016   [Refereed]
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 fam...
Atsufumi Honda
Kyushu Journal of Mathematics   70(2) 217-226   Sep 2016   [Refereed]
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 admissi...
Atsufumi Honda, Shyuichi Izumiya
Journal of Geometry   106(1) 185-210   Apr 2015   [Refereed]
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 diff...
Masaru Hasegawa, Atsufumi Honda, Kosuke Naokawa, Kentaro Saji, Masaaki Umehara, Kotaro Yamada
International Journal of Mathematics   26(4) 1540008   Mar 2015   [Refereed]
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 ...
Masaru Hasegawa, Atsufumi Honda, Kosuke Naokawa, Masaaki Umehara, Kotaro Yamada
Selecta Mathematica. New Series   20(3) 769-785   Jul 2014   [Refereed]
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...
Atsufumi Honda, Miyuki Koiso, Yasuhiro Tanaka
Journal of Math-for-Industry   5(A) 73-82   Apr 2013   [Refereed]
Atsufumi Honda
RIMS Ko^kyu^roku Bessatsu   B38 169-187   Apr 2013   [Refereed]
Atsufumi Honda
Tohoku Mathematical Journal, Second Series   64(2) 171-193   Jun 2012   [Refereed]
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 verti...


Atsufumi Honda
   Aug 2019
A connected regular surface in Lorentz-Minkowski 3-space is called a mixed
type surface if the spacelike, timelike and lightlike point sets are all
non-empty. Lightlike points on mixed type surfaces may be regarded as singular
points of the induce...
Shintaro Akamine, Atsufumi Honda, Masaaki Umehara, Kotaro Yamada
   Jul 2019
Calabi and Cheng-Yau's Bernstein-type theorem asserts that an entire zero
mean curvature graph in Lorentz-Minkowski Tex-space Tex
which admits only space-like points is a hyperplane. Recently, the third and
fourth authors p...
Atsufumi Honda, Kosuke Naokawa, Kentaro Saji, Masaaki Umehara, Kotaro Yamada
   Jun 2019
In the second, fourth and fifth authors' previous work, a duality on generic
real analytic cuspidal edges in the Euclidean 3-space Tex
preserving their singular set images and first fundamental forms, was given. In
this paper, we sho...
HONDA Atsufumi
   May 2019
In Lorentz-Minkowski 3-space, the fundamental theorem of spacelike curves is known, if they have spacelike, timelike or lightlike curvature vector fields. However, such a theory cannot be applied to spacelike curves with type-changing curvature ve...
Atsufumi Honda, Kentaro Saji, Keisuke Teramoto
   Nov 2018
A mixed type surface is a connected regular surface in a Lorentzian
3-manifold with non-empty spacelike and timelike point sets. The induced metric
of a mixed type surface is a signature-changing metric, and their lightlike
points may be regarded ...
Atsufumi Honda, Kentaro Saji
   Oct 2017
We introduce two invariants called the secondary cuspidal curvature and the
bias on Tex-cuspidal edges, and investigate their basic properties. While the
secondary cuspidal curvature is an analog of the cuspidal curvature of
(ordinary) cuspidal ...
Atsufumi Honda, Kosuke Naokawa, Masaaki Umehara, Kotaro Yamada
   Oct 2017
Cuspidal edges and swallowtails are typical non-degenerate singular points on wave fronts in the Euclidean 3-space. Their first fundamental forms belong to a class of positive semi-definite metrics called `Kossowski metrics'. A point where a Kosso...
Transformations and orientability of extrinsically flat surfaces
Atsufumi HONDA
Progress in Surface Theory, Mathematisches Forschungsinstitut Oberwolfach      May 2013