Geodesic mappings of quasi-Einstein spaces with a constant scalar curvature

  • V. A. Kiosak Institute of Engineering Odesa State Academy of Civil Engineering and Architecture, Ukraine
  • G. V. Kovalova Institute of Engineering Odesa State Academy of Civil Engineering and Architecture, Ukraine
Keywords: pseudo-Riemannian spaces; quasi-Einstein spaces; geodesic mapping

Abstract

In this paper we study a special type of pseudo-Riemannian spaces - quasi-Einstein spaces of constant scalar curvature. These spaces are generalizations of known Einstein spaces. We obtained a linear form of the basic equations of the theory of geodetic mappings for these spaces. The studies are conducted locally in tensor form, without restrictions on the sign and signature of the metric tensor.

Author Biographies

V. A. Kiosak, Institute of Engineering Odesa State Academy of Civil Engineering and Architecture, Ukraine

Institute of Engineering Odesa State Academy of Civil Engineering and Architecture, Ukraine

G. V. Kovalova, Institute of Engineering Odesa State Academy of Civil Engineering and Architecture, Ukraine

Institute of Engineering Odesa State Academy of Civil Engineering and Architecture, Ukraine

References

E. Beltrami, Risoluzione del problema: riportari i punti di una superficie sopra un piano in modo che le linee geodetiche vengano rappresentante da linee rette, Ann. Mat., 1 (1865), 7, 185-204.

U. Dini, Sobre un problema che is presenta nella theoria generale delle rappresentazioni geografiche diuna supeficie su di un'altra, Ann. Mat., 2 (1869), III, 269-293.

L. Evtushik, V. Kiosak, J. Mikes, The mobility of Riemannian spaces with respect to conformal mappings onto Einstein spaces, Russian Mathematics, 54(2010), 29-33.

A. Fedorova, V. Kiosak, V. Matveev, S. Rosemann, The only Kahler manifold with degree of mobility at least 3 is (CP(n), g Fubini-Study), Proceedings of the London Mathematical Society, 2012; https://doi.org/10.1112/plms/pdr053.

G. Fubini, Sui gruppi transformazioni geodetiche, Mem. Acad.Sci.Torino, 53(1903), 2, 261-313.

V. A. Kiosak, On the conformal mappings of quasi-Einstein spaces, Journal of Mathematical Sciences, United States, 184(2012), 12-18.

V. Kiosak, I. Hinterleitner, φ(Ric)-Vector Fields on Conformally Flat Spaces, Proceedings of American Institute of Physics, 98(2009), 1191, 98-103, https://doi.org/10.1063/1.3275604.

V.A. Kiosak, I. Hinterleitner, φ(Ric)-Vector Fields in Riemannian Spaces , Archivum-mathematicum, Brno, 44(2008), 385-390.

V. Kiosak, I. Hinterleitner, Special Einstein's equations on Kahler manifolds, Archivum Mathematicum,

(2010), 5, 333-337.

V. Kiosak, O. Lesechko, O. Savchenko, Mappings of Spaces with Affine Connection, 17th Conference on Applied Mathematics, APLIMAT 2018 - Procedings, Bratislava, 2018, 563-569.

V. Kiosak, V. Matveev, There exist no 4-dimensional geodesically equivalent metrics with the same stress-energy tensor, Journal of Geometry and Physics, 78(2014), 1-11.

V.A. Kiosak, V.S. Matveev, J. Mikeš, I.G. Shandra, On the degree of geodesic mobility for Riemannian metrics , Mathematical Notes, 87(2010), 4, 586-587.

V. Kiosak, O. Savchenko, O. Gudyreva, On the conformal mappings of special quasi-Einstein spaces, AIP Conference Procedings, 2164, 040001 (2019); https://doi.org/10.1063/1.5130793.

V. Kiosak, O. Savchenko, T. Shevchenko, Holomorphically Projective Mappings of Special Kahler Manifolds, AIP Conference Procedings, 2025, 08004(2018); https://doi.org/10.1063/1.5064924.

J. L. Lagrange, Sur la construction des cartes geographiques, Noveaux Memoires de l'Academie des Sciences et Bell-Lettres de Berlin, 1779.

T. Levi-Civita, Sulle transformationi delle equazioni dinamiche, Ann. Mat. Milano, 2(1896), 24, 255-300.

J. Mikes, I. Hinterleitner, V A. Kiosak, On the Theory of Geodesic Mappings of Einstein Spaces and their Generalizations, AIP Conference Proceedings, 861, 428 (2006); https://doi.org/10.1063/1.2399606.

N.S. Sinyukov, Geodesic mappings of Riemannian spaces, Nauka, (1979), 255p. (in Russian)

Published
2020-06-24
How to Cite
1.
Kiosak VA, Kovalova GV. Geodesic mappings of quasi-Einstein spaces with a constant scalar curvature. Mat. Stud. [Internet]. 2020Jun.24 [cited 2020Jul.6];53(2):212-7. Available from: http://matstud.org.ua/ojs/index.php/matstud/article/view/13
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Articles