Umbilic foliations with integrable normal bundle

In this paper we study the geometric properties of a couple of mutually orthogonal foliations with complementary dimensions. We recall that from Novikov's theorem, there is no foliation of S3 by closed curves with integrable normal bundle. Nevertheless, for S2k+1, k≥2, Novikov's theorem is...

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Bibliographic Details
Published in:Bulletin des sciences mathématiques 2017-08, Vol.141 (6), p.573-583
Main Authors: de Almeida, S.C., Brito, F.G.B., Colares, A.G.
Format: Article
Language:English
Subjects:
Foliations
Mean curvature vector
Normal bundle
Umbilic foliations
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Summary:In this paper we study the geometric properties of a couple of mutually orthogonal foliations with complementary dimensions. We recall that from Novikov's theorem, there is no foliation of S3 by closed curves with integrable normal bundle. Nevertheless, for S2k+1, k≥2, Novikov's theorem is not applicable. In this paper we show that on odd-dimensional unit spheres there is no umbilical foliation with integrable normal bundle and divergence free mean curvature vector.
ISSN:0007-4497
1952-4773
DOI:10.1016/j.bulsci.2017.05.002