Algebraic Integrability Conditions for Killing Tensors on Constant Sectional Curvature Manifolds

Abstract

We use an isomorphism between the space of valence two Killing tensors on an n-dimensional constant sectional curvature manifold and the irreducible GL(n+1)-representation space of algebraic curvature tensors in order to translate the Nijenhuis integrability conditions for a Killing tensor into purely algebraic integrability conditions for the corresponding algebraic curvature tensor, resulting in two simple algebraic equations of degree two and three. As a first application of this we construct a new family of integrable Killing tensors.

34 pages, no figures

References in corpus (3)

• Quasi-Lagrangian Systems of Newton Equations
• Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
• Equivalence problem for the orthogonal webs on the sphere

Cited by in corpus (7)

• Invariant classification of second-order conformally flat superintegrable systems
• The Variety of Integrable Killing Tensors on the 3-Sphere
• An Algebraic Geometric Foundation for a Classification of Superintegrable Systems in Arbitrary Dimension
• A special class of symmetric Killing 2-tensors
• Are Orthogonal Separable Coordinates Really Classified?
• Separation coordinates, moduli spaces and Stasheff polytopes
• Nijenhuis Integrability for Killing Tensors