Directed Riemannian manifolds of pointwise constant relative sectional curvature
Differential Geometry
2014-11-14 v1
Abstract
We study a class of Riemannian manifolds with respect to the covariant derivative of their curvature tensors. We introduce geometrically the class of directed Riemannian manifolds of pointwise constant relative sectional curvature and give a tensor characterization for such manifolds. We prove that all rotational hypersurfaces are directed and find the rotational hypersurfaces of pointwise constant relative sectional curvature. For the class of directed Riemannian manifolds of pointwise constant relative sectional curvature having a totally umbilical scalar distribution we prove a structural theorem and a theorem of Schur's type.
Keywords
Cite
@article{arxiv.1307.0918,
title = {Directed Riemannian manifolds of pointwise constant relative sectional curvature},
author = {Georgi Ganchev and Vesselka Mihova},
journal= {arXiv preprint arXiv:1307.0918},
year = {2014}
}
Comments
10 pages