Conformal and Geodesic Mappings onto Some Special Spaces
1
Department of Mathematics and Physics, Uman National University of Horticulture, 20300 Uman, Ukraine
2
Department of Economic Cybernetics and Information Technologies, Odesa National Economic University, 65082 Odesa, Ukraine
3
Department of Algebra and Geometry, Faculty of Science, Palacky University in Olomouc, 771 46 Olomouc, Czech Republic
4
Department of Mathematics, Faculty of Civil Engineering, Brno University of Technology, 601 90 Brno, Czech Republic
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(8), 664; https://doi.org/10.3390/math7080664
Received: 21 June 2019 / Revised: 22 July 2019 / Accepted: 23 July 2019 / Published: 25 July 2019
(This article belongs to the Special Issue Differential Geometry of Special Mappings)
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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Keywords:
space with affine connection; riemannian space; ricci-m-symmetric space; conformal mapping; geodesic mapping
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
MDPI and ACS Style
Berezovski, V.; Cherevko, Y.; Rýparová, L. Conformal and Geodesic Mappings onto Some Special Spaces. Mathematics 2019, 7, 664.
AMA Style
Berezovski V, Cherevko Y, Rýparová L. Conformal and Geodesic Mappings onto Some Special Spaces. Mathematics. 2019; 7(8):664.
Chicago/Turabian StyleBerezovski, Volodymyr; Cherevko, Yevhen; Rýparová, Lenka. 2019. "Conformal and Geodesic Mappings onto Some Special Spaces" Mathematics 7, no. 8: 664.
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