Proceedings of the International Conference on Geometry, Integrability and Quantization

A Recursion Operator for the Geodesic Flow on N-Dimensional Sphere

Kiyonori Hosokawa

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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 $S^n$.

Article information

Source
Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Andrei Ludu and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2014), 152-161

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815708

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

Mathematical Reviews number (MathSciNet)
MR

Zentralblatt MATH identifier

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