Argument shift method and sectional operators: applications to differential geometry

TL;DR

This paper explores a systematic construction linking integrable systems on Lie algebras with the study of projectively equivalent Riemannian metrics, highlighting connections between these mathematical areas.

Contribution

It presents a unified approach to relate concepts from integrable systems and differential geometry without introducing new results.

Findings

Establishes a relationship between integrable systems and projectively equivalent metrics

Provides a systematic construction connecting different mathematical ideas

Highlights the interdisciplinary nature of the topics involved

Abstract

This paper does not contain any new results, it is just an attempt to present, in a systematic way, one construction which establishes an interesting relationship between some ideas and notions well-known in the theory of integrable systems on Lie algebras and a rather different area of mathematics studying projectively equivalent Riemannian and pseudo-Riemannian metrics.