CONFORMAL VECTOR FIELDS ON TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD

Abstract

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