Degree of the Gauss map and curvature integrals for closed hypersurfaces
Differential Geometry
2016-09-16 v1
Abstract
Given a unit vector field on a closed Euclidean hypersurface, we define a map from the hypersurface to a sphere in the Euclidean space. This application allows us to exhibit a list of topological invariants which combines the second fundamental form of the hypersurface and the vector field itself. We show how these invariants can be used as obstructions to certain codimension one foliations.
Cite
@article{arxiv.1609.04670,
title = {Degree of the Gauss map and curvature integrals for closed hypersurfaces},
author = {Fabiano G. B. Brito and Icaro Gonçalves},
journal= {arXiv preprint arXiv:1609.04670},
year = {2016}
}