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arXiv · 0811.3478

Hidden symmetries and Killing tensors on curved spaces

Stere Ianus·Mihai Visinescu·Gabriel-Eduard Vilcu
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Abstract

Higher order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. One presents the infinite dimensional superalgebra of Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be seen as a twisted loop algebra. The existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed Sasakian structures.

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Stere Ianus, Mihai Visinescu, Gabriel-Eduard Vilcu. 2008-11-21. Hidden symmetries and Killing tensors on curved spaces. https://doi.org/10.1134/s1063778810110141

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