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Article

Geodesic Mappings of Vn(K)-Spaces and Concircular Vector Fields

1
Department of Data Analysis, Decision-Making and Financial Technology, Financial University under the Government of the Russian Federation, Leningradsky Prospect 49-55, Moscow 125468, Russia
2
Department of Algebra and Geometry, Palacky University, 17. listopadu 12, 77146 Olomouc, Czech Republic
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(8), 692; https://doi.org/10.3390/math7080692
Received: 18 July 2019 / Revised: 30 July 2019 / Accepted: 31 July 2019 / Published: 1 August 2019
(This article belongs to the Special Issue Differential Geometry of Special Mappings)
In the present paper, we study geodesic mappings of special pseudo-Riemannian manifolds called V n ( K ) -spaces. We prove that the set of solutions of the system of equations of geodesic mappings on V n ( K ) -spaces forms a special Jordan algebra and the set of solutions generated by concircular fields is an ideal of this algebra. We show that pseudo-Riemannian manifolds admitting a concircular field of the basic type form the class of manifolds closed with respect to the geodesic mappings. View Full-Text
Keywords: pseudo-Riemannian manifold; Jordan algebra; concircular vector field; geodesic mapping pseudo-Riemannian manifold; Jordan algebra; concircular vector field; geodesic mapping
MDPI and ACS Style

Shandra, I.G.; Mikeš, J. Geodesic Mappings of Vn(K)-Spaces and Concircular Vector Fields. Mathematics 2019, 7, 692. https://doi.org/10.3390/math7080692

AMA Style

Shandra IG, Mikeš J. Geodesic Mappings of Vn(K)-Spaces and Concircular Vector Fields. Mathematics. 2019; 7(8):692. https://doi.org/10.3390/math7080692

Chicago/Turabian Style

Shandra, Igor G., and Josef Mikeš. 2019. "Geodesic Mappings of Vn(K)-Spaces and Concircular Vector Fields" Mathematics 7, no. 8: 692. https://doi.org/10.3390/math7080692

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