8 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…