Algebraic Integrability Conditions for Killing Tensors on Constant Sectional Curvature Manifolds

Details Algebraic Integrability Conditions for Killing Tensors on Constant Sectional Curvature Manifolds Algebraic Integrability Conditions for Killing Tensors on Constant Sectional Curvature Manifolds

2010-04-16

arxiv.org/abs/1004.2872v1

Mathematics

Differential Geometry

34 pages, no figures

Scientific paper

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.

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