# Geodesic mappings and concircular vector fields

## TL;DR

This paper investigates geodesic mappings of $V_n(K)$-spaces and reveals algebraic structures and invariance properties related to concircular vector fields in pseudo-Riemannian geometry.

## Contribution

It demonstrates that solutions to geodesic mappings form a Jordan algebra and that manifolds with concircular fields are closed under these mappings.

## Key findings

- Solutions form a Jordan algebra
- Concircular fields generate an ideal in the algebra
- Manifolds with concircular fields are closed under geodesic mappings

## 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.