Killing-Yano Tensors of Order n-1

Abstract

The properties of a Killing-Yano tensor of order n-1 in an n-dimensional manifold are investigated. The integrability conditions are worked out and all metrics admitting a Killing-Yano tensor of order n-1 are found. It is pointed out a connection between such tensors and a generalization of the concept of angular momentum. A theorem on how to generate closed conformal Killing vectors using the symmetries of a manifold is proved and used to find all Killing-Yano tensors of order n-1 of a maximally symmetric space.

arXiv comment15 pages. Published Version

References in corpus (15)

• Classification of the Weyl Tensor in Higher Dimensions
• Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
• Separability of Hamilton-Jacobi and Klein-Gordon Equations in General Kerr-NUT-AdS Spacetimes
• Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
• Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions
• Dirac symmetry operators from conformal Killing-Yano tensors
• Separability of Dirac equation in higher dimensional Kerr-NUT-de Sitter spacetime
• Higher dimensional VSI spacetimes
• Debye Potentials for Maxwell and Dirac Fields from a Generalisation of the Killing-Yano Equation
• A Rainich-like approach to the Killing-Yano tensors
• On the geometry of Killing and conformal tensors
• Isometries in higher dimensional CCNV spacetimes
• On the Weyl Tensor Classification in All Dimensions and its Relation with Integrability Properties
• On the space-times admitting two shear-free geodesic null congruences
• Schouten-Nijenhuis bracket of Killing-Yano tensors for Kimura IIC metric

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• New currents with Killing-Yano tensors
• Finsler gravitational waves of $(\alpha ,\beta )$-type and their observational signature
• General first-order mass ladder operators for Klein-Gordon fields
• A Class of Integrable Metrics
• Integrability Conditions for Killing-Yano Tensors and Maximally Symmetric Spaces in the Presence of Torsion
• Symmetries and conserved quantities with arbitrary torsion: A generalization of Killing's theorem
• Doppler shift in semi-Riemannian signature and the non-uniqueness of the Krein space of spinors
• A Class of Integrable Metrics II