Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 023, 18 pages      arXiv:1511.00234      https://doi.org/10.3842/SIGMA.2016.023
Contribution to the Special Issue on Analytical Mechanics and Differential Geometry in honour of Sergio Benenti

Haantjes Structures for the Jacobi-Calogero Model and the Benenti Systems

Giorgio Tondo a and Piergiulio Tempesta bc
a) Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, piaz.le Europa 1, I-34127 Trieste, Italy
b) Departamento de Física Teórica II, Facultad de Físicas, Universidad Complutense, 28040 - Madrid, Spain
c) Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/ Nicolás Cabrera, No 13-15, 28049 Madrid, Spain

Received November 03, 2015, in final form February 22, 2016; Published online March 03, 2016

Abstract
In the context of the theory of symplectic-Haantjes manifolds, we construct the Haantjes structures of generalized Stäckel systems and, as a particular case, of the quasi-bi-Hamiltonian systems. As an application, we recover the Haantjes manifolds for the rational Calogero model with three particles and for the Benenti systems.

Key words: Haantjes tensor; symplectic-Haantjes manifolds; Stäckel systems; quasi-bi-Hamiltonian systems; Benenti systems.

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