Degree of the Gauss map and curvature integrals for closed hypersurfaces

Fabiano G. B. Brito; Icaro Gonçalves

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arXiv · 1609.04670

Degree of the Gauss map and curvature integrals for closed hypersurfaces

Fabiano G. B. Brito·Icaro Gonçalves

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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.

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BibTeX RIS

Fabiano G. B. Brito, Icaro Gonçalves. 2016-09-15. Degree of the Gauss map and curvature integrals for closed hypersurfaces. https://arxiv.org/abs/1609.04670

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