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Relationships between behavior of the Gaussian curvature at a cuspidal edge and types of singularities of the corresponding Gauss map

Hold Date 2019-05-17 16:00~2019-05-17 17:00

Place Lecture Room L W1-D-313, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Keisuke TERAMOTO (Kyushu University)

A (wave) front is a class of surfaces with singularities, and a cuspidal edge is a typical singularity of a front. It is known that fronts admit unit normal vector fields or Gauss maps even at singularities. Recently, several differential geometric invariants at a cuspidal edge are defined and relations between behavior of the Gaussian curvature and these invariants at that point are investigated. Moreover, the Gaussian curvature diverges near a cuspidal edge in general, but it is known that the set of singular points of the Gauss map coincides with the set consisting of cuspidal edges when the Gaussian curvature is (nonzero) bounded near a cuspidal edge. In this talk, I explain relation between types of singularities of the Gauss map of a surface with cuspidal edges and behavior of the Gaussian curvature if the Gaussian curvature is nonzero bounded. Moreover, I show relation between signs of the Gaussian curvature and geometric invariants of a cuspidal edge when the Gauss map has
certain singularities.

* This seminar is combined with Topology Seminar.