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

被引：9

作者：

Berezovski, Volodymyr ^{[1
]}

Cherevko, Yevhen ^{[2
]}

Hinterleitner, Irena ^{[3
]}

Peska, Patrik ^{[4
]}

机构：

[1] Uman Natl Univ Hort, Dept Math & Phys, UA-20300 Uman, Ukraine

[2] Odesa Natl Acad Food Technol, Dept Phys & Math Sci, UA-65039 Odesa, Ukraine

[3] Brno Univ Technol, Inst Math & Descript Geometry, Brno 60200, Czech Republic

[4] Palacky Univ Olomouc, Dept Algebra & Geometry, Olomouc 77147, Czech Republic

来源：

MATHEMATICS | 2020年 / 8卷 / 09期

关键词：

geodesic mapping; space with an affine connection; m-symmetric space; m-Ricci-symmetric space; INVARIANTS; MANIFOLDS;

D O I：

10.3390/math8091560

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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-, andm- (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. Anym- (Ricci-) symmetric spaces (m >= 1) are geodesically mapped onto many spaces with an affine connection. We can call these spacesprojectivelly m- (Ricci-) symmetric spacesand for them there exist above-mentioned nontrivial solutions.

引用

页数：13

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