On canonical F-planar mappings of spaces with affine connection

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.

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

Filomat ◽

10.2298/fil1914475b ◽

2019 ◽

Vol 33 (14) ◽

pp. 4475-4480 ◽

Cited By ~ 1

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

Mathematics ◽

10.3390/math8091560 ◽

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.

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Geodesic mappings of manifolds with affine connection onto the Ricci symmetric manifolds

Filomat ◽

10.2298/fil1802379b ◽

2018 ◽

Vol 32 (2) ◽

pp. 379-385 ◽

Cited By ~ 2

Author(s):

Volodymyr Berezovskii ◽

Irena Hinterleitner ◽

Josef Mikes

Keyword(s):

Ricci Tensor ◽

Fundamental System ◽

Affine Connection ◽

Cauchy Type ◽

Covariant Derivatives

In the present paper we investigate geodesic mappings of manifolds with affine connection onto Ricci symmetric manifolds which are characterized by the covariantly constant Ricci tensor. 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 n(n+1) real parameters. Analogous results are obtained for geodesic mappings of manifolds with affine connection onto symmetric manifolds.

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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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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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On semisymmetric connection

Filomat ◽

10.2298/fil1904179v ◽

2019 ◽

Vol 33 (4) ◽

pp. 1179-1184

Author(s):

Ana Velimirovic ◽

Milan Zlatanovic

Keyword(s):

Symmetric Space ◽

Curvature Tensor ◽

The Other ◽

Linear Combinations ◽

Covariant Derivatives ◽

Linearly Independent ◽

Curvature Tensors

Using the non-symmetry of a connection, it is possible to introduce four types of covariant derivatives. Based on these derivatives, several types of Ricci?s identities and twelve curvature tensors are obtained. Five of them are linearly independent but the other curvature tensors can be expressed as linear combinations of these five linearly independent curvature tensors and the curvature tensor of the corresponding associated symmetric space. The semisymmetric connection is defined and the properties of two of the five independent curvature tensors are analyzed. In the same manner, the properties for three others curvature tensors may be derived.

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Conformai Curvature Tensors

The Ambient Metric (AM-178) ◽

10.23943/princeton/9780691153131.003.0006 ◽

2011 ◽

Author(s):

Charles Fefferman ◽

C. Robin Graham

Keyword(s):

Normal Form ◽

Curvature Tensor ◽

Riemannian Metric ◽

Conformal Group ◽

Conformal Change ◽

Conformal Curvature ◽

Covariant Derivatives ◽

Curvature Tensors ◽

Derivatives Of

This chapter studies conformal curvature tensors of a pseudo-Riemannian metric g. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form relative to g. Their transformation laws under conformal change are given in terms of the action of a subgroup of the conformal group O(p + 1, q + 1) on tensors. It is assumed throughout this chapter that n ≥ 3.

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Covariant derivatives on Kähler C-spaces

Nagoya Mathematical Journal ◽

10.1017/s0027763000005912 ◽

1996 ◽

Vol 143 ◽

pp. 31-57

Author(s):

Koji Tojo

Keyword(s):

Curvature Tensor ◽

Covariant Derivatives ◽

Civita Connection ◽

Levi Civita Connection

Let (M, g) be a Kähler C-space. R and ∇ denote the curvature tensor and the Levi-Civita connection of (M, g), respectively.In [6], Takagi have proved that there exists an integer n such that

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