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VOL. 15 | 2014 A Recursion Operator for the Geodesic Flow on N-Dimensional Sphere
Kiyonori Hosokawa

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka

Abstract

For a completely integrable system, the way of finding first integrals is not formulated in general. A new characterization for integrable systems using the particular tensor field is investigated which is called a recursion operator. A recursion operator $T$ for a vector field $\Delta$ is a diagonizable $(1, 1)$-type tensor field, invariant under $\Delta$ and has vanishing Nijenhuis torsion. One of the important property of $T$ is that $T$ gives constants of the motion (the sequence of first integrals) for the vector field $\Delta$. The purpose of this paper is to discuss a recursion operator $T$ for the geodesic flow on $S^n$.

Information

Published: 1 January 2014
First available in Project Euclid: 13 July 2015

zbMATH: 1343.53084
MathSciNet: MR3287755

Digital Object Identifier: 10.7546/giq-15-2014-152-161

Rights: Copyright © 2014 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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