CONFORMAL VECTOR FIELDS ON TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD

Document Type: Research Note

Authors

Faculty of Mathematics, Amir-Kabir University of Technology, Hafez Ave. 15914, Tehran, I. R. of Iran

Abstract

Let M be an n-dimensional Riemannian manifold and TM its tangent bundle. The
conformal and fiber preserving vector fields on TM have well-known physical interpretations and have
been studied by physicists and geometricians. Here we define a Riemannian or pseudo-Riemannian lift
metric g􀀄 on TM , which is in some senses more general than other lift metrics previously defined on
TM , and seems to complete these works. Next we study the lift conformal vector fields on (TM,g􀀄) and
prove among the others that, every complete lift conformal vector field on TM is homothetic, and
moreover, every horizontal or vertical lift conformal vector field on TM is a Killing vector.

Keywords