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arXiv · 1004.2872

Algebraic Integrability Conditions for Killing Tensors on Constant Sectional Curvature Manifolds

Konrad P. Schöbel
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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.

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BibTeXRIS

Konrad P. Schöbel. 2010-04-16. Algebraic Integrability Conditions for Killing Tensors on Constant Sectional Curvature Manifolds. https://doi.org/10.1016/j.geomphys.2012.01.006

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