Orthogonal foliations on riemannian manifolds

2017/11/15 by Gomes, André de Oliveira, da Silva, Eurípedes Carvalho
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.05690

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, F and 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 F and F^\bot, if one of the foliations is totally umbilical. We also prove an integral formula for such foliations.

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