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Degree of the Gauss Map and Curvature Integrals for Closed Hypersurfaces

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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 invariants which combines the second fundamental form of the hypersurface and the covariant derivative of the vector field. We show how these invariants can be used as obstructions to the existence of codimension one foliations with prescribed geometric properties.

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Authors and Affiliations

  1. Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, Santo André, SP, 09.210-170, Brazil

    Fabiano Gustavo Braga Brito

  2. Dpto. de Matemática, Instituto de Matemática e Estatística, Universidade de Sāo Paulo, R. do Matāo 1010, Sāo Paulo, SP, 05508-900, Brazil

    Icaro Gonçalves

Authors
  1. Fabiano Gustavo Braga Brito
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  2. Icaro Gonçalves
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Corresponding author

Correspondence to Icaro Gonçalves.

Additional information

During the preparation of this paper the second author was supported by CNPq, 141113/2013-8, Brazil.

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Brito, F.G.B., Gonçalves, I. Degree of the Gauss Map and Curvature Integrals for Closed Hypersurfaces. Results Math 73, 70 (2018). https://doi.org/10.1007/s00025-018-0832-7

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  • DOI: https://doi.org/10.1007/s00025-018-0832-7

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