On geodesic mappings preserving the Einstein tensor

Olena E. Chepurna; Volodymyr A. Kiosak; Josef Mikeš

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2010)

  • Volume: 49, Issue: 2, page 49-52
  • ISSN: 0231-9721

Abstract

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In this paper there are discussed the geodesic mappings which preserved the Einstein tensor. We proved that the tensor of concircular curvature is invariant under Einstein tensor-preserving geodesic mappings.

How to cite

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Chepurna, Olena E., Kiosak, Volodymyr A., and Mikeš, Josef. "On geodesic mappings preserving the Einstein tensor." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 49.2 (2010): 49-52. <http://eudml.org/doc/116513>.

@article{Chepurna2010,
abstract = {In this paper there are discussed the geodesic mappings which preserved the Einstein tensor. We proved that the tensor of concircular curvature is invariant under Einstein tensor-preserving geodesic mappings.},
author = {Chepurna, Olena E., Kiosak, Volodymyr A., Mikeš, Josef},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Geodesic mapping; Einstein tensor; geodesic mapping; Einstein tensor},
language = {eng},
number = {2},
pages = {49-52},
publisher = {Palacký University Olomouc},
title = {On geodesic mappings preserving the Einstein tensor},
url = {http://eudml.org/doc/116513},
volume = {49},
year = {2010},
}

TY - JOUR
AU - Chepurna, Olena E.
AU - Kiosak, Volodymyr A.
AU - Mikeš, Josef
TI - On geodesic mappings preserving the Einstein tensor
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2010
PB - Palacký University Olomouc
VL - 49
IS - 2
SP - 49
EP - 52
AB - In this paper there are discussed the geodesic mappings which preserved the Einstein tensor. We proved that the tensor of concircular curvature is invariant under Einstein tensor-preserving geodesic mappings.
LA - eng
KW - Geodesic mapping; Einstein tensor; geodesic mapping; Einstein tensor
UR - http://eudml.org/doc/116513
ER -

References

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  1. Chepurna, O., Kiosak, V., Mikeš, J, Conformal mappings of Riemannian spaces which preserve the Einstein tensor, J. Appl. Math. Aplimat 3, 1 (2010), 253–258. (2010) 
  2. Mikeš, J., 10.1007/BF01709156, Math. Notes 28 (1981), 922–923, Translation of Mat. Zametki 28 (1980), 935–938. (1981) MR0603226DOI10.1007/BF01709156
  3. Mikeš, J., 10.1007/BF02365193, J. Math. Sci. 78, 3 (1996), 311–333. (1996) MR1384327DOI10.1007/BF02365193
  4. Mikeš, J., Hinterleitner, I., Kiosak, V., On the theory of geodesic mappings of Einstein spaces and their generalizations, AIP Conf. Proc. 861 (2006), 428–435. (2006) 
  5. Mikeš, J., Kiosak, V. A., Vanžurová, A., Geodesic mappings of manifolds with affine connection, Palacky University Press, Olomouc, 2008. (2008) Zbl1176.53004MR2488821
  6. Mikeš, J., Vanžurová, A., Hinterleitner, I., Geodesic mappings and some generalizations, Palacky University Press, Olomouc, 2009. (2009) Zbl1222.53002MR2682926
  7. Sinyukov, N. S., Geodesic mappings of Riemannian spaces, Nauka, Moscow, 1979. (1979) Zbl0637.53020MR0552022
  8. Yano, K., Concircular Geometry, Proc. Imp. Acad. 16 (Tokyo), (1940), 195–200, 354–360, 442–448, 505–511. (1940) Zbl0025.08504

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