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

Igor G. Shandra and Josef Mikeš
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Igor G. Shandra: 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
Josef Mikeš: Department of Algebra and Geometry, Palacky University, 17. listopadu 12, 77146 Olomouc, Czech Republic

Mathematics, 2019, vol. 7, issue 8, 1-11

Abstract: 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.

Keywords: pseudo-Riemannian manifold; Jordan algebra; concircular vector field; geodesic mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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