Conformal vector fields on Finsler spaces

Abstract

Here, it is shown that every vector field on a Finsler space which keeps geodesic circles invariant is conformal. A necessary and sufficient condition for a vector field to keep geodesic circles invariant, known as concircular vector fields, is obtained. This leads to a significant definition of concircular vector fields on a Finsler space. Finally, complete Finsler spaces admitting a special conformal vector field are classified.