PreprintarXiv licencearXiv
A convexity theorem for proper Dupin hypersurfaces in spheres
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.
Related
- An improved second pinching theorem for minimal hypersurfaces with constant scalar curvature in spheres
- Analyticity and tautness of smooth Dupin hypersurfaces
- Curvature pinching for minimal Tangent-Yang-Mills hypersurfaces in spheres
- Shades and Convexity of Hypersurfaces
- Spheres with transitive families of CMC hypersurfaces
BibTeX
@misc{mare2026convexity,
title = {{A convexity theorem for proper Dupin hypersurfaces in spheres}},
author = {Augustin-Liviu Mare},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36366},
eprint = {2610.36366},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36366},
}
RIS
TY - UNPB
TI - A convexity theorem for proper Dupin hypersurfaces in spheres
AU - Augustin-Liviu Mare
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36366
UR - https://arxiv.org/abs/2610.36366
AB - 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.
ER -