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

@article{Tondo2016HaantjesSF, title={Haantjes Structures for the Jacobi-Calogero Model and the Benenti Systems}, author={G. Tondo and P. Tempesta}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2016}, volume={12}, pages={023} }

In the context of the theory of symplectic-Haantjes manifolds, we construct the Haantjes structures of generalized Stackel 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.

#### 12 Citations

Haantjes Algebras of the Lagrange Top

- Mathematics, Physics
- 2018

We study a symplectic-Haantjes manifold and a Poisson–Haantjes manifold for the Lagrange top and compute a set of Darboux–Haantjes coordinates. Such coordinates are separation variables for the… Expand

Beyond recursion operators

- Mathematics
- 2019

We briefly recall the history of the Nijenhuis torsion of (1, 1)-tensors on manifolds and of the lesser-known Haantjes torsion. We then show how the Haantjes manifolds of Magri and the symplectic… Expand

Classical Multiseparable Hamiltonian Systems, Superintegrability and Haantjes Geometry

- Physics, Mathematics
- 2020

We show that the theory of classical Hamiltonian systems admitting separation variables can be formulated in the context of (ω,H ) structures. They are essentially symplectic manifolds endowed with a… Expand

Haantjes algebras and diagonalization

- Mathematics, Physics
- 2021

Abstract We introduce the notion of Haantjes algebra: It consists of an assignment of a family of operator fields on a differentiable manifold, each of them with vanishing Haantjes torsion. They are… Expand

Higher Haantjes Brackets and Integrability

- Mathematics
- 2018

We propose a new, infinite class of brackets generalizing the Frölicher– Nijenhuis bracket. This class can be reduced to a family of generalized Nijenhuis torsions recently introduced. In particular,… Expand

A New Class of Generalized Haantjes Tensors and Nilpotency

- Mathematics
- 2018

We propose a new infinite class of generalized binary tensor fields. The first representative of this class is the known Fr\"olicher--Nijenhuis bracket. Also, this new family of tensors reduces to… Expand

H O ] 2 4 D ec 2 01 7 Beyond recursion operators

- 2018

We briefly recall the history of the Nijenhuis torsion of (1, 1)-tensors on manifolds and of the lesser-known Haantjes torsion. We then show how the Haantjes manifolds of Magri and the… Expand

A New family of higher-order Generalized Haantjes Tensors, Nilpotency and Integrability

- Mathematics
- 2018

We propose a new infinite class of generalized binary tensor fields, whose first representative of is the known Frolicher--Nijenhuis bracket. This new family of tensors reduces to the generalized… Expand

An approach for obtaining integrable Hamiltonians from Poisson-commuting polynomial families

- Mathematics, Physics
- 2017

We discuss a general approach permitting the identification of a broad class of sets of Poisson-commuting Hamiltonians, which are integrable in the sense of Liouville. It is shown that all such… Expand

Constructing a Complete Integral of the Hamilton–Jacobi Equation on Pseudo-Riemannian Spaces with Simply Transitive Groups of Motions

- Mathematics, Physics
- 2019

In this work, a method for constructing a complete integral of the geodesic Hamilton-Jacobi equation on pseudo-Riemannian manifolds with simply transitive actions of groups of motions is suggested.… Expand

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