Totally Geodesic Submanifolds in Tangent Bundle with g - natural Metric
Differential Geometry
2015-06-17 v1
Abstract
In the paper we investigate submanifolds in a tangent bundle endowed with g-natural metric G, defined by a vector field on a base manifold. We give a sufficient condition for a vector field on M to defined totally geodesic submanifold in (TM,G). The parallel vector field is discussed in more detail.
Keywords
Cite
@article{arxiv.1310.8606,
title = {Totally Geodesic Submanifolds in Tangent Bundle with g - natural Metric},
author = {Stanisław Ewert-Krzemieniewski},
journal= {arXiv preprint arXiv:1310.8606},
year = {2015}
}
Comments
Key words: Riemannian manifold, submanifold, tangent bundle, g - natural metric, totally geodesic, Sasaki metric