Submanifolds with nonparallel first normal bundle revisited
Differential Geometry
2013-06-20 v2
Abstract
In this paper, we analyze the geometric structure of an Euclidean submanifold whose osculating spaces form a nonconstant family of proper subspaces of the same dimension. We prove that if the rate of change of the osculating spaces is small, then the submanifold must be a (submanifold of a) ruled submanifold of a very special type. We also give a sharp estimate of the dimension of the rulings.
Keywords
Cite
@article{arxiv.1105.0808,
title = {Submanifolds with nonparallel first normal bundle revisited},
author = {Marcos Dajczer and Ruy Tojeiro},
journal= {arXiv preprint arXiv:1105.0808},
year = {2013}
}
Comments
11 pages. Final version. To appear in Pub. Mat