Riemannian geometry of fibre bundles

Abstract

CONTENTS Introduction § 1. Riemannian and pseudo-Riemannian metrics on fibre bundles § 2. Riemannian submersions 2.1. Main equations of a Riemannian submersion 2.2. Geodesics in Riemannian submersions § 3. Connection between the geometric features of the tangent bundle (the normal bundle) and the base § 4. Geodesic lines in the tangent and normal bundles. Totally geodesic submanifolds 4.1. The Sasaki geodesic metrics of the tangent bundle 4.2. The geodesics of the Sasaki metric of the normal bundle § 5. Surfaces in the tangent bundle of a Riemannian manifold § 6. Certain geometric applications of the Sasaki metric § 7. Questions and problems References References on Riemannian geometry