Geodesically equivalent metrics and Nijenhuis geometry

A. V. Bolsinov<sup>ab

a</sup> Department of Mathematical Sciences, Loughborough University, Loughborough, UK
^b Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Abstract: We show how concepts, methods and results from Nijenhuis geometry can be used to study geodesically equivalent metrics. We propose a new method of the presentation and proof of many facts in the classical theory of geodesically equivalent metrics and develop methods for the further development of this theory.
Bibliography: 33 titles.

Keywords: geodesically equivalent metrics, Nijenhuis operator, geodesic flow, symmetries, conservation laws.

MSC: Primary 53B20, 53C15; Secondary 53D17, 70H06

Received: 20.10.2024 and 13.01.2025

DOI: 10.4213/sm10220

 English version: Sbornik: Mathematics, 2025, 216:5, 583–607

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