Algebraic integrability conditions for Killing tensors on constant sectional curvature manifolds |
| |
Authors: | Konrad P Schöbel |
| |
Institution: | Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, 07737 Jena, Germany |
| |
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. |
| |
Keywords: | Killing tensors Integrability Constant sectional curvature manifolds |
本文献已被 ScienceDirect 等数据库收录! |