Geodesic mappings of spaces with affine connnection onto generalized Ricci symmetric spaces

Berezovski, Volodymyr; Mikeš, Josef; Rýparová, Lenka

doi:10.2298/fil1914475b

Cited by 2 publications

(2 citation statements)

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“…Refs. [46][47][48] were devoted to geodesic mappings of spaces with an affine connections onto Ricci-symmetric and 2-Ricci-symmetric spaces. The main equations for the mappings were also obtained as closed systems of PDE's of Cauchy type.…”

Section: Basic Concepts Of the Theory Of Geodesic Mappings Of Spaces With Affine Connectionsmentioning

confidence: 99%

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Geodesic Mappings of Spaces with Affine Connections onto Generalized Symmetric and Ricci-Symmetric Spaces

et al. 2020

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In the paper, we consider geodesic mappings of spaces with an affine connections onto generalized symmetric and Ricci-symmetric spaces. In particular, we studied in detail geodesic mappings of spaces with an affine connections onto 2-, 3-, and m- (Ricci-) symmetric spaces. These spaces play an important role in the General Theory of Relativity. The main results we obtained were generalized to a case of geodesic mappings of spaces with an affine connection onto (Ricci-) symmetric spaces. The main equations of the mappings were obtained as closed mixed systems of PDEs of the Cauchy type in covariant form. For the systems, we have found the maximum number of essential parameters which the solutions depend on. Any m- (Ricci-) symmetric spaces (m≥1) are geodesically mapped onto many spaces with an affine connection. We can call these spaces projectivelly m- (Ricci-) symmetric spaces and for them there exist above-mentioned nontrivial solutions.

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Section: Basic Concepts Of the Theory Of Geodesic Mappings Of Spaces With Affine Connectionsmentioning

confidence: 99%

“…For geodesic mappings of generalized symmetric and recurrent spaces, such problems were solved by J. Mikeš, V.S. Sobchuk, and others [21][22][23][24][25][26][27][38][39][40][41][42][43][44][45][46][47][48]. There are many works devoted to issues of the theory of geodesic mappings, for example [49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%