Helix, shadow boundary and minimal submanifolds
Differential Geometry
2007-06-12 v1
Abstract
Inspired by a Blaschke's work about analytic convex surfaces, we study {\em shadow boundaries} of Riemannian submanifolds , which are defined by a parallel vector field along . Since a shadow boundary is just a closed subset of , first, we will give a condition that guarantee its smoothness. It depends on the second fundamental form of the submanifold. It is natural to search for what kind of properties might have such submanifolds of ? Could they be totally geodesic or minimal? Answers to these and related questions are given in this work.
Cite
@article{arxiv.0706.1524,
title = {Helix, shadow boundary and minimal submanifolds},
author = {Gabriel Ruiz-Hernandez},
journal= {arXiv preprint arXiv:0706.1524},
year = {2007}
}