10 citations · 45 across the 27 of their papers we have counts for
29 papers
Isometric deformations of pillow boxes
Atsufumi Honda, Miyuki Koiso
Pillow boxes are surfaces used for gift boxes, packaging, and even architectural applications. By definition, a pillow box is isometric to a double rectangle consisting of two copi…
Mannheim-d'Ocagne-Koenderink type formulas for asymptotic directions
Toshizumi Fukui, Atsufumi Honda, Masaaki Umehara
We consider a surface embedded in the Euclidean 3-space and fix a tangential vector at a given point on the surface. In this paper, we first review a history of the formula…
Null hypersurfaces as wave fronts in Lorentz-Minkowski space
Shintaro Akamine, Atsufumi Honda, Masaaki Umehara +1
In this paper, we show that ``-complete null hypersurfaces'' (i.e. ruled hypersurfaces foliated by entirety of light-like lines) as wave fronts in the -dimensional Lorent…
Symmetries of cross caps
Atsufumi Honda, Kosuke Naokawa, Kentaro Saji +2
It is well-known that cross caps on surfaces in the Euclidean 3-space can be expressed in Bruce-West's normal form, which is a special local coordinate system centered at the singu…
A generalization of Zakalyukin's lemma, and symmetries of surface singularities
Atsufumi Honda, Kosuke Naokawa, Kentaro Saji +2
Zakalyukin's lemma asserts that the coincidence of the images of two wave front germs implies the right equivalence of corresponding map germs under a certain genericity assumption…
Singularities of spacelike mean curvature one surfaces in de Sitter space
Atsufumi Honda, Himemi Sato
In this paper, we study the singularities of spacelike constant mean curvature one (CMC 1) surfaces in the de Sitter 3-space. We prove the duality between generalized conelike sing…
Geometry of lightlike locus on mixed type surfaces in Lorentz-Minkowski 3-space from a contact viewpoint
Atsufumi Honda, Shyuichi Izumiya, Kentaro Saji +1
A surface in the Lorentz-Minkowski -space is generally a mixed type surface, namely, it has the lightlike locus. We study local differential geometric properties of such a locus…
Heinz-type mean curvature estimates in Lorentz-Minkowski space
Atsufumi Honda, Yu Kawakami, Miyuki Koiso +1
We provide a unified description of Heinz-type mean curvature estimates under an assumption on the gradient bound for space-like graphs and time-like graphs in the Lorentz-Minkowsk…
On the existence of four or more curved foldings with common creases and crease patterns
Atsufumi Honda, Kosuke Naokawa, Kentaro Saji +2
Consider an oriented curve in a domain in the plane . Thinking of as a piece of paper, one can make a curved folding in the Euclidean space $\boldsymbo…
Null hypersurfaces in Lorentzian manifolds with the null energy condition
Shintaro Akamine, Atsufumi Honda, Masaaki Umehara +1
Let be a light-like geodesically complete Lorentzian -manifold satisfying the null energy condition. We show that null hypersurfaces properly immersed in $M^{n+1…
Curved foldings with common creases and crease patterns
Atsufumi Honda, Kosuke Naokawa, Kentaro Saji +2
Consider a curve in a domain in the plane . Thinking of as a piece of paper, one can make a curved folding in the Euclidean space …
Isometric deformations of mixed type surfaces in Lorentz-Minkowski space
Atsufumi Honda
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 m…
Cuspidal edges with the same first fundamental forms along a knot
Atsufumi Honda, Kosuke Naokawa, Kentaro Saji +2
Letting be a compact -curve embedded in ( means real analyticity), we consider a -cuspidal edge along . When is non-closed, in the a…
Bernstein-type theorem for zero mean curvature hypersurfaces without time-like points in Lorentz-Minkowski space
Shintaro Akamine, Atsufumi Honda, Masaaki Umehara +1
Calabi and Cheng-Yau's Bernstein-type theorem asserts that an entire zero mean curvature graph in Lorentz-Minkowski -space which admits only space-li…
Duality on generalized cuspidal edges preserving singular set images and first fundamental forms
Atsufumi Honda, Kosuke Naokawa, Kentaro Saji +2
In the second, fourth and fifth authors' previous work, a duality on generic real analytic cuspidal edges in the Euclidean 3-space preserving their singular set i…
Behavior of torsion functions of spacelike curves in Lorentz-Minkowski space
Atsufumi Honda
In this paper, we introduce the pseudo-torsion functions along spacelike curves whose curvature vector field has isolated lightlike points in Lorentz-Minkowski 3-space, and prove t…
Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds
Atsufumi Honda, Kentaro Saji, Keisuke Teramoto
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 sig…
Geometric invariants of -cuspidal edges
Atsufumi Honda, Kentaro Saji
We introduce two invariants called the secondary cuspidal curvature and the bias on -cuspidal edges, and investigate their basic properties. While the secondary cuspidal curva…
Isometric deformations of wave fronts at non-degenerate singular points
Atsufumi Honda, Kosuke Naokawa, Masaaki Umehara +1
Cuspidal edges and swallowtails are typical non-degenerate singular points on wave fronts in the Euclidean -space. Their first fundamental forms belong to a class of positive se…
Complete flat fronts as hypersurfaces in Euclidean space
Atsufumi Honda
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 no…
Minimal Darboux transformations
U. Hertrich-Jeromin, A. Honda
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 D…
Isometric realization of cross caps as formal power series and its applications
Atsufumi Honda, Kosuke Naokawa, Masaaki Umehara +1
Two cross caps in Euclidean -space are said to be formally isometric if their Taylor expansions of the first fundamental forms coincide by taking a suitable local coordinate sys…
Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space
Atsufumi Honda, Miyuki Koiso, Kentaro Saji
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…
Isometric immersions with singularities between space forms of the same positive curvature
Atsufumi Honda
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…