Singularities of Gauss maps of wave fronts with non-degenerate singular points
Volume 69 / 2021
Bulletin Polish Acad. Sci. Math. 69 (2021), 149-169
MSC: Primary 57R45; Secondary 53A05, 58K05.
DOI: 10.4064/ba200820-13-11
Published online: 30 November 2021
Abstract
We study singularities of Gauss maps of (wave) fronts and give characterizations of singularities of Gauss maps by geometric properties of fronts which are related to behavior of bounded principal curvatures. Moreover, we investigate the relation between a kind of boundedness of Gaussian curvatures near cuspidal edges and types of singularities of their Gauss maps. Further, we consider extended height functions on fronts with non-degenerate singular points.
