scholarly journals Conformal and Geodesic Mappings onto Some Special Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 664 ◽  
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.

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

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}.

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

Mathematics ◽  
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.

scholarly journals On Canonical Almost Geodesic Mappings of Type π2(e)

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 54 ◽  
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.

Conformal Mappings of Riemannian Spaces onto Ricci Symmetric Spaces

2018 ◽  
Vol 103 (1-2) ◽  
pp. 304-307 ◽  
Author(s):  
V. E. Berezovskii ◽  
I. Hinterleitner ◽  
N. I. Guseva ◽  
J. Mikeš
Keyword(s):  
Symmetric Spaces ◽  
Conformal Mappings ◽  
Riemannian Spaces

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

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1560
Author(s):  
Volodymyr Berezovski ◽  
Yevhen Cherevko ◽  
Irena Hinterleitner ◽  
Patrik Peška
Keyword(s):  
Symmetric Spaces ◽  
Affine Connection ◽  
Cauchy Type ◽  
Theory Of Relativity ◽  
Covariant Form ◽  
General Theory Of Relativity ◽  
Nontrivial Solutions ◽  
Affine Connections ◽  
Systems Of Pdes ◽  
Mixed Systems

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.

scholarly journals On almost geodesic mappings of the second type between manifolds with non-symmetric linear connection

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3831-3841 ◽  
Author(s):  
Milos Petrovic ◽  
Mica Stankovic
Keyword(s):  
Special Class ◽  
Linear Connection ◽  
Cauchy Type ◽  
Symmetric Part ◽  
Covariant Derivatives ◽  
Affinor Structure ◽  
Derivatives Of ◽  
Mixed Systems ◽  
Riemannian Spaces

We derive two mixed systems of Cauchy type in covariant derivatives of the first and second kind that ensures the existence of almost geodesic mappings of the second type between manifolds with non-symmetric linear connection. Also, we consider a particular class of these mappings determined by the condition ?F = 0, where ? is the symmetric part of non-symmetric linear connection ?1 and F is the affinor structure. The same special class of almost geodesic mappings of the second type between generalized Riemannian spaces was recently considered in the paper (M.Z. Petrovic, Special almost geodesic mappings of the second type between generalized Riemannian spaces, Bull. Malays. Math. Sci. Soc. (2), DOI :10.1007/s40840-017-0509-5)

scholarly journals On canonical F-planar mappings of spaces with affine connection

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1273-1278
Author(s):  
Volodymyr Berezovski ◽  
Josef Mikes ◽  
Patrik Peska ◽  
Lenka Rýparová
Keyword(s):  
General Solution ◽  
Curvature Tensor ◽  
Symmetric Spaces ◽  
Affine Connection ◽  
Cauchy Type ◽  
Partial Differential ◽  
Covariant Derivatives ◽  
Type Form

In this paper we study the theory of F-planar mappings of spaces with affine connection. We obtained condition, which preserved the curvature tensor. We also studied canonical F-planar mappings of space with affine connection onto symmetric spaces. In this case, the main equations have the partial differential Cauchy type form in covariant derivatives. We got the set of substantial real parameters on which depends the general solution of that PDE?s system.

scholarly journals On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 626 ◽  
Author(s):  
Miloš Z. Petrović ◽  
Mića S. Stanković ◽  
Patrik Peška
Keyword(s):  
Symmetric Spaces ◽  
Covariant Derivatives ◽  
Derivatives Of ◽  
Riemannian Spaces

We consider conformal and concircular mappings of Eisenhart’s generalized Riemannian spaces. We prove conformal and concircular invariance of some tensors in Eisenhart’s generalized Riemannian spaces. We give new generalizations of symmetric spaces via Eisenhart’s generalized Riemannian spaces. Finally, we describe some properties of covariant derivatives of tensors analogous to Yano’s tensor of concircular curvature in Eisenhart symmetric spaces of various kinds.

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

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4475-4480 ◽  
Author(s):  
V.E. Berezovski ◽  
Josef Mikes ◽  
Lenka Rýparová
Keyword(s):  
Symmetric Spaces ◽  
Fundamental System ◽  
Affine Connection ◽  
Cauchy Type ◽  
Covariant Derivatives

The presented work is devoted to study of the geodesic mappings of spaces with affine connection onto generalized Ricci symmetric spaces. We obtained a fundamental system for this problem in a form of a system of Cauchy type equations in covariant derivatives depending on no more than 1/2 n2(n+1)+n real parameters. Analogous results are obtained for geodesic mappings of manifolds with affine connection onto equiaffine generalized Ricci symmetric spaces.

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