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Argument shift method and sectional operators: applications to differential geometry

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journal contribution
posted on 29.02.2016, 10:07 authored by Alexey BolsinovAlexey Bolsinov
This text does not contain any new results, it is just an attempt to present, in a systematic way, one construction which makes it possible to use some ideas and notions well-known in the theory of integrable systems on Lie algebras to a rather different area of mathematics related to the study of projectively equivalent Riemannian and pseudo-Riemannian metrics. The main observation can be formulated, yet without going into details, as follows: The curvature tensors of projectively equivalent metrics coincide with the Hamiltonians of multi-dimensional rigid bodies. Such a relationship seems to be quite interesting and may apparently have further applications in differential geometry. The wish to talk about this relation itself (rather than some new results) was one of motivations for this paper.



  • Science


  • Mathematical Sciences

Published in

Fundamental and Applied Mathematics


BOLSINOV, A., 2017. Argument shift method and sectional operators: applications to differential geometry. Fundamental and Applied Mathematics, 20 (3), pp.5-31.


Center of New Information Technologies, Moscow State University


AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date



This paper was accepted for publication in the journal Fundamental and Applied Mathematics.