Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connections onto Generalized m-Ricci-Symmetric Spaces

Volodymyr Berezovski; Yevhen Cherevko; Josef Mikeš; Lenka Rýparová

doi:10.3390/math9040437

Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connections onto Generalized m-Ricci-Symmetric Spaces

Mathematics ◽

10.3390/math9040437 ◽

2021 ◽

Vol 9 (4) ◽

pp. 437

Author(s):

Volodymyr Berezovski ◽

Yevhen Cherevko ◽

Josef Mikeš ◽

Lenka Rýparová

Keyword(s):

Differential Equations ◽

Closed System ◽

Symmetric Spaces ◽

Linear Differential Equations ◽

Cauchy Type ◽

Affine Connections ◽

Covariant Derivatives ◽

Linear Differential

In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces. In either case the main equations for the mappings are obtained as a closed system of linear differential equations of Cauchy type in the covariant derivatives. The obtained results extend an amount of research produced by N.S. Sinyukov, V.E. Berezovski, J. Mikeš.

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Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connection Onto Generalized 2-Ricci-Symmetric Spaces

Geometry Integrability and Quantization ◽

10.7546/giq-22-2021-78-87 ◽

2021 ◽

Vol 22 ◽

pp. 78-87

Author(s):

Volodymyr Berezovski ◽

Yevhen Cherevko ◽

Svitlana Leshchenko ◽

Josef Mikes

Keyword(s):

Differential Equations ◽

Closed System ◽

Symmetric Spaces ◽

Affine Connection ◽

Linear Differential Equations ◽

Cauchy Type ◽

Affine Connections ◽

Covariant Derivatives ◽

Linear Differential

In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces. The main equations for the mappings are obtained as a closed system of linear differential equations of Cauchy type in the covariant derivatives. The obtained result extends an amount of research produced by Sinyukov, Berezovski and Mike\v{s}.

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Conformal and Geodesic Mappings onto Some Special Spaces

Mathematics ◽

10.3390/math7080664 ◽

2019 ◽

Vol 7 (8) ◽

pp. 664 ◽

Cited By ~ 2

Author(s):

Volodymyr Berezovski ◽

Yevhen Cherevko ◽

Lenka Rýparová

Keyword(s):

Differential Equations ◽

Closed System ◽

Symmetric Spaces ◽

Conformal Mappings ◽

Cauchy Type ◽

Affine Connections ◽

Covariant Derivatives ◽

Riemannian Spaces

In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of Cauchy-type differential equations in covariant derivatives. We find the number of essential parameters which the solution of the system depends on. A similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces, as well as geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.

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On Canonical Almost Geodesic Mappings of Type π2(e)

Mathematics ◽

10.3390/math8010054 ◽

2020 ◽

Vol 8 (1) ◽

pp. 54 ◽

Cited By ~ 1

Author(s):

Volodymyr Berezovski ◽

Josef Mikeš ◽

Lenka Rýparová ◽

Almazbek Sabykanov

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Symmetric Spaces ◽

Riemann Tensor ◽

Mixed System ◽

Cauchy Type ◽

Partial Differential ◽

Affine Connections

In the paper, we consider canonical almost geodesic mappings of type π 2 ( e ) . We have found the conditions that must be satisfied for the mappings to preserve the Riemann tensor. Furthermore, we consider canonical almost geodesic mappings of type π 2 ( e ) of spaces with affine connections onto symmetric spaces. The main equations for the mappings are obtained as a closed mixed system of Cauchy-type Partial Differential Equations. We have found the maximum number of essential parameters which the solution of the system depends on.

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