10 citations · 25 across the 11 of their papers we have counts for
12 papers
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…
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…
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 …
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…
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…
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…
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…
Intrinsic properties of surfaces with singularities
Masaru Hasegawa, Atsufumi Honda, Kosuke Naokawa +3
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 metri…
Isometric deformations of cuspidal edges
Kosuke Naokawa, Masaaki Umehara, Kotaro Yamada
Along cuspidal edge singularities on a given surface in Euclidean 3-space, which can be parametrized by a regular space curve, a unit normal vector field is well-defined as a s…
Intrinsic Invariants of Cross Caps
Masaru Hasegawa, Atsufumi Honda, Kosuke Naokawa +2
It is classically known that generic smooth maps of R^2 into R^3 admit only cross cap singularities. This suggests that the class of cross caps might be an important object in diff…
Singularities of the asymptotic completion of developable Möbius strips
Kosuke Naokawa
We prove that the asymptotic completion of a developable Möbius strip in Euclidean three-space must have at least one singular point other than cuspidal edge singularities. Moreove…