Differential geometry of tangent bundles, with applications to harmonic maps.

摘要

This thesis is about the geometry of the tangent bundle TM of a Riemannian manifold M. We study different metrics on TM and the geodesics and harmonic maps with respect to these metrics. Some examples and consequences are discussed when M = S{dollar}sp n{dollar}.; In particular, we concentrate on certain embeddings {dollar}TSsp2to X{dollar} for different spaces X, and we examine the induced metric. Finally, we discuss some special examples of harmonic maps, namely "homogeneous" harmonic maps from S{dollar}sp2{dollar} to {dollar}TSsp2.{dollar}