Geodesic Mappings of Semi-Riemannian Manifolds with a Degenerate Metric

Igor G. Shandra and Josef Mikeš
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Igor G. Shandra: Department of Mathematics, Financial University under the Goverment the Russian Federation, 125468 Moscow, Russia
Josef Mikeš: Department of Algebra and Geometry, Faculty of Science, Palacky University, 771 46 Olomouc, Czech Republic

Mathematics, 2022, vol. 10, issue 1, 1-11

Abstract: This article introduces the concept of geodesic mappings of manifolds with idempotent pseudo-connections. The basic equations of canonical geodesic mappings of manifolds with completely idempotent pseudo-connectivity and semi-Riemannian manifolds with a degenerate metric are obtained. It is proved that semi-Riemannian manifolds admitting concircular fields admit completely canonical geodesic mappings and form a closed class with respect to these mappings.

Keywords: semi-Riemannian manifold; degenerate metric; pseudo-connection; concircular vector field; geodesic mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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