Geodesic
Conformally geodesic mappings satisfying a certain initial condition
Archivum mathematicum, Tome 47 (2011) no. 5, pp. 389-394 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $f\colon M \rightarrow \bar{M}$ 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.
In this paper we study conformally geodesic mappings between pseudo-Riemannian manifolds $(M, g)$ and $(\bar{M}, \bar{g})$, i.e. mappings $f\colon M \rightarrow \bar{M}$ 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.
Classification : 53B20, 53B30, 53C21
Keywords: conformal mappings; geodesic mappings; conformally geodesic mappings 
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     url = {http://geodesic.mathdoc.fr/item/ARM_2011_47_5_a5/}
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Chudá, Hana; Mikeš, Josef. Conformally geodesic mappings satisfying a certain initial condition. Archivum mathematicum, Tome 47 (2011) no. 5, pp. 389-394. http://geodesic.mathdoc.fr/item/ARM_2011_47_5_a5/

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