Algebraic integrability conditions for Killing tensors on constant sectional curvature manifolds

作者：Schoebel Konrad P

来源：Journal of Geometry and Physics, 2012, 62(5): 1013-1037.

DOI：10.1016/j.geomphys.2012.01.006

• Killing tensors
• Integrability
• Constant sectional curvature manifolds

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.

• 出版日期2012-5