Advanced Search

In this paper we study conformally geodesic mappings between pseudo-Riemannian manifolds $(M,g)$ and $(\overline{M},\overline{g})$, i.e. mappings $f:M\to \overline{M}$ satisfying $f=f_1\circ f_2\circ f_3$, where $f_1,f_3$ are conformal mappings and $f_2$ is a geodesic mapping. Suppose that the initial condition $f^{*}\overline{g}=kg$ is satisfied at a point $x_0\in M$ and that at this point the conformal Weyl tensor does not vanish. We prove that then $f$ is necessarily conformal.