Totally Geodesic Submanifolds in Tangent Bundle with g - natural Metric

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.

arXiv commentKey words: Riemannian manifold, submanifold, tangent bundle, g - natural metric, totally geodesic, Sasaki metric