Conformal Vector Fields on Tangent Bundle of a Riemannian Manifold

Details Conformal Vector Fields on Tangent Bundle of a Riemannian Manifold Conformal Vector Fields on Tangent Bundle of a Riemannian Manifold

2006-07-15

arxiv.org/abs/math/0607360v1

Iranian Journal of Science & Technology, Transaction A, Vol. 29, No. A3, 2005

Mathematics

Differential Geometry

Scientific paper

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 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 its tangent bundle with this metric 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.

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