Year: 2026
Type: preprint
Abstract: We prove that if $M$ is a (compact, connected, and embedded) proper Dupin hypersurface in a sphere then, viewing $M$ as a submanifold of the ambient Euclidean space, its orthogonal projection to the normal space at any point is convex. This is a generalization of the convexity theorem of Terng for isoparametric submanifolds in Euclidean spaces.
Source: arXiv (Cornell University)
Author: Mare, Augustin-Liviu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224076998