INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION

Abstract

The main purpose of the present paper is to study properties of vertical infinitesimal affine transformation in the tangent bundle of a Riemannian manifold with respect to the horizontal lift of an affine connection, and to apply the results obtained to the study of fibre-preserving infinitesimal affine transformations in this setting.