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
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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
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MDPI and ACS Style
Berezovski, V.; Cherevko, Y.; Rýparová, L. Conformal and Geodesic Mappings onto Some Special Spaces. Mathematics 2019, 7, 664.
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