Vector fields generating certain special transformations

Zbigniew Olszak

Displaying similar documents to “Vector fields generating certain special transformations”

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In this paper we study conformally geodesic mappings between pseudo-Riemannian manifolds $(M, g)$ and $(\bar{M}, \bar{g})$ , i.e. mappings $f : M \to \bar{M}$ 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 $f^{*} \bar{g} = k g$ 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.