Conformally geodesic mappings satisfying a certain initial condition

Hana Chudá; Josef Mikeš

Archivum Mathematicum (2011)

  • Volume: 047, Issue: 5, page 389-394
  • ISSN: 0044-8753

Abstract

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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 ∘ f 2 ∘ f 3 , where f 1 , f 3 are conformal mappings and f 2 is a geodesic mapping. Suppose that the initial condition f * g ¯ = k g is satisfied 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.

How to cite

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Chudá, Hana, and Mikeš, Josef. "Conformally geodesic mappings satisfying a certain initial condition." Archivum Mathematicum 047.5 (2011): 389-394. <http://eudml.org/doc/247183>.

@article{Chudá2011,
abstract = {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.},
author = {Chudá, Hana, Mikeš, Josef},
journal = {Archivum Mathematicum},
keywords = {conformal mappings; geodesic mappings; conformally geodesic mappings; conformal mapping; geodesic mapping; conformally geodesic mapping},
language = {eng},
number = {5},
pages = {389-394},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Conformally geodesic mappings satisfying a certain initial condition},
url = {http://eudml.org/doc/247183},
volume = {047},
year = {2011},
}

TY - JOUR
AU - Chudá, Hana
AU - Mikeš, Josef
TI - Conformally geodesic mappings satisfying a certain initial condition
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 5
SP - 389
EP - 394
AB - 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.
LA - eng
KW - conformal mappings; geodesic mappings; conformally geodesic mappings; conformal mapping; geodesic mapping; conformally geodesic mapping
UR - http://eudml.org/doc/247183
ER -

References

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  9. Mikeš, J., Vanžurová, A., Hinterleitner, I., Geodesic mappings and some generalizations, Palacky University Press, Olomouc, 2009. (2009) Zbl1222.53002MR2682926
  10. Petrov, A. Z., New methods in the general theory of relativity, Nauka, Moscow, 1966. (1966) MR0207365
  11. Sinyukov, N. S., Geodesic mappings of Riemannian spaces, Nauka, Moscow, 1979. (1979) Zbl0637.53020MR0552022
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