Integral formulas for a metric-affine manifold with two complementary orthogonal distributions
Differential Geometry
2019-11-21 v2
Abstract
We obtain integral formulas for a metric-affine space equipped with two complementary orthogonal distributions. The integrand depends on the Ricci and mixed scalar curvatures and invariants of the second fundamental forms and integrability tensors of the distributions. The formulas under some conditions yield splitting of manifolds (including submersions and twisted products) and provide geometrical obstructions for existence of distributions and foliations (or compact leaves of them).
Cite
@article{arxiv.1612.03272,
title = {Integral formulas for a metric-affine manifold with two complementary orthogonal distributions},
author = {Vladimir Rovenski},
journal= {arXiv preprint arXiv:1612.03272},
year = {2019}
}
Comments
11 pages