Fiber-Preserving Conformal Vector Field of Frame Bundles with Natural Riemannian Metric

Abstract

We consider the bundle of all oriented orthonormal frames over an orientable Remannian manifold. This bundle has a natural Riemannian metric which is defined by the Riemannian connection of the base manifold. The purpose of the present paper is to classify the conformal vector field structure of the frame bundle with natural Riemannian metric.

Keywords

• bundle of all oriented orthonormal frames
• conformal vector field