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.
Highlights
The problem of geodesic mappings of the pseudo-Riemannian manifold was first studied byLevi-Civita [1]
In the present paper, we study geodesic mappings of special pseudo-Riemannian manifolds called Vn (K )-spaces
We prove that the set of solutions of the system of equations of geodesic mappings on Vn (K )-spaces forms a special Jordan algebra and the set of solutions generated by concircular fields is an ideal of this algebra
Summary
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 Department of Algebra and Geometry, Palacky University, 17. listopadu 12, 77146 Olomouc, Czech Republic
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