Orthogonal foliations on riemannian manifolds

André de Oliveira Gomes; Eurípedes Carvalho da Silva

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arXiv · 1711.05690

Orthogonal foliations on riemannian manifolds

André de Oliveira Gomes·Eurípedes Carvalho da Silva

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Abstract

In this work, we find an equation that relates the Ricci curvature of a riemannian manifold $M$ and the second fundamental forms of two orthogonal foliations of complementary dimensions, $\mathcal{F}$ and $\mathcal{F}^{\bot}$, defined on $M$. Using this equation, we show a sufficient condition for the manifold M to be locally a riemannian product of the leaves of $\mathcal{F}$ and $\mathcal{F}^{\bot}$, if one of the foliations is totally umbilical. We also prove an integral formula for such foliations.

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BibTeX RIS

André de Oliveira Gomes, Eurípedes Carvalho da Silva. 2017-11-15. Orthogonal foliations on riemannian manifolds. https://arxiv.org/abs/1711.05690

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