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.

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.

scholarly journals Of one over determined system differential equations at private derivative second order with one singular lines in general case

2021 ◽  
pp. 10-15
Author(s):  
Boitura Shoimkulov ◽  
◽  
Р. М. С. Lukmon ◽  
Keyword(s):  
Partial Differential Equations ◽  
Initial Data ◽  
Differential Equations ◽  
Compatibility Condition ◽  
Second Order ◽  
Integral Representations ◽  
Singular Line ◽  
Cauchy Type ◽  
Partial Differential

In this paper, an over determined system of second-order partial differential equations with a single singular line in the General case is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with a single singular line in the General case. If the compatibility condition is met, integral representations of the variety of solutions are found explicitly in terms of three arbitrary constants, when the singular line is in the boundaries of the domain for which initial data problems (Cauchy-type Problems) can be set.

Some second-order systems of partial differential equations of composite type

1987 ◽  
Vol 106 (1-2) ◽  
pp. 73-88 ◽  
Author(s):  
Lin Wei
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hyperbolic Systems ◽  
Second Order ◽  
Cauchy Type ◽  
Linear Transformations ◽  
Partial Differential ◽  
Composite Systems ◽  
Composite Type ◽  
Second Order Systems

SynopsisThe Cauchy problem and the Dirichlet-Cauchy type problem of some second-order systems of partial differential equations of composite type of two unknown functions are investigated. Such systems possess some of the characteristics not only of elliptic but also of hyperbolic systems in the same domain. Representations of the solutions are found for the upper half plane. To this end, the composite systems are reduced to the canonical form by means of successive applications of three kinds of linear transformations. Function theoretic methods are used to obtain representation formulae. Furthermore, some composite systems of 2m-unknown function are also considered.

scholarly journals Integral representation of solution manifolds for over determined systems with one singular line

2021 ◽  
pp. 5-9
Author(s):  
Boitura Shoimkulov ◽  
Keyword(s):  
Partial Differential Equations ◽  
Initial Data ◽  
Differential Equations ◽  
Integral Representation ◽  
Compatibility Condition ◽  
Second Order ◽  
Singular Line ◽  
Cauchy Type ◽  
Partial Differential ◽  
Partial Differential System

In this paper, an over determined system of second-order partial differential equations with one singular line is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with one singular line. Under the condition of compatibility, introducing a new function, we come to a over determined system of partial differential equations of the second order with one singular line of a simpler form. The integral representation of the manifold of solutions of the redefined second-order partial differential system with one singular line is found explicitly through three arbitrary constants, for which initial data problems (Cauchy type problems) can be posed.

scholarly journals Of one over determined system differential equation at private derivative second order with one singular point and one singular line

2021 ◽  
pp. 14-18
Author(s):  
B. M. Shoimkulov ◽  
Keyword(s):  
Partial Differential Equations ◽  
Singular Point ◽  
Differential Equations ◽  
Compatibility Condition ◽  
Second Order ◽  
Integral Representations ◽  
Singular Line ◽  
Cauchy Type ◽  
National Academy Of Sciences ◽  
Partial Differential

In this paper, a over determined system of second-order partial differential equations with one singular point and one singular line is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with one singular point and one singular line. If the compatibility condition is met, integral representations of the variety of solutions are found explicitly in terms of three arbitrary constants, when the singular line is in the boundaries of the domain for which initial data problems (Cauchy-type Problems) can be set. In this paper considers a redefined system of second-order partial differential equations, when the coefficients and right parts have one singular point and one singular line. Obtaining a variety of solutions and studying boundary value problems for linear differential equations of the hyperbolic type of the second order, some linear redefined systems of the first and second order with one and two supersingular lines and supersingular points is devoted to the monograph of academician of the National Academy of Sciences of the Republic of Tatarstan Rajabov N. - 1992 "Introduction to the theory of partial differential equations with supersingular coefficients" [6, p.126]. Using the obtained results of The monograph of Rajabov N., a variety of solutions of redefined systems of partial differential equations of the second order with one singular point and one singular line in an explicit form, through three arbitrary constants, was found.

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}.

NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS ON HOMOGENEOUS SPACES

1990 ◽  
Vol 05 (09) ◽  
pp. 1801-1817 ◽  
Author(s):  
M. GÜRSES ◽  
Ö. OǦUZ ◽  
S. SALIHOǦLU
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symmetric Spaces ◽  
Homogeneous Spaces ◽  
Nonlinear Partial Differential Equations ◽  
Lie Superalgebras ◽  
Partial Differential

The work of A.K.N.S. which is based on the sl(2, R) valued soliton connection is extended to obtain new integrable coupled nonlinear partial differential equations. This is achieved by assuming the soliton connection having values in a simple Lie, Kac-Moody, Lie superalgebras. Extensions of some of the integrable nonlinear partial differential equations are given explicitly. In particular the coupled NLS equations on various homogeneous spaces and the coupled modified KdV integro-differential equations are obtained on symmetric spaces.

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.

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