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arXiv · 1905.02818

Geodesic mappings and concircular vector fields

Igor G. Shandra
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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 $(K\neq0)$ forms a special Jordan algebra and the set of solutions generated by consircular 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.

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Igor G. Shandra. 2019-05-07. Geodesic mappings and concircular vector fields. https://arxiv.org/abs/1905.02818

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