3 papers
math.DG2025
Explicit analytic functions defining the images of wave-front singularities
Kentaro Saji, Masaaki Umehara, Kotaro Yamada
We give explicit real-analytic functions whose zero sets characterize the images of the standard maps of wave-front singularities. Such functions are realizations of the main-analy…
math.DG2024
Deformations of swallowtails in a 3-dimensional space form
Kentaro Saji, Masaaki Umehara, Kotaro Yamada
This is a continuation of the authors' earlier work on deformations of cuspidal edges. We give a representation formula for swallowtails in the Euclidean 3-space. Using this, we in…
math.DG2024
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…