Conformally geodesic mappings satisfying a certain initial condition

Abstract

In this paper we study conformally geodesic mappings between pseudo-Riemannian manifolds (M,g) and (M,g), i.e. mappings f:M→M satisfying f = f; 1 o f; 2 o f; 3, where f; 1, f3 are conformal mappings and f; 2 is a geodesic mapping. Suppose that the initial condition f*g = kg is satisfed at a point x; 0 ∈ M and that at this point the conformal Weyl tensor does not vanish. We prove that then f is necessarily conformal.