Killing-Yano tensors and some applications

Abstract

The role of Killing and Killing-Yano tensors for studying the geodesic motion of the particle and the superparticle in a curved background is reviewed. Additionally the Papadopoulos list [74] for Killing-Yano tensors in G structures is reproduced by studying the torsion types these structures admit. The Papadopoulos list deals with groups G appearing in the Berger classification, and we enlarge the list by considering additional G structures which are not of the Berger type. Possible applications of these results in the study of supersymmetric particle actions and in the AdS/CFT correspondence are outlined.

36 pages, no figures

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• Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
• Notes on Super Killing Tensors
• Local metrics admitting a principal Killing-Yano tensor with torsion
• Geometry of Lax pairs: particle motion and Killing-Yano tensors
• Symmetry operators and decoupled equations for linear fields on black hole spacetimes
• Integrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors
• Rational first integrals of geodesic equations and generalised hidden symmetries
• New currents with Killing-Yano tensors
• Symmetry operators of Killing spinors and superalgebras in AdS_5
• Killing-Yano Cotton Currents
• A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
• Tensionless Strings and Killing(-Yano) Tensors
• Uses of Killing and Killing-Yano Tensors
• Killing-Yano symmetry of Kaluza-Klein black holes in five dimensions
• Twisted form hierarchies, Killing-Yano equations and supersymmetric backgrounds
• A Class of Integrable Metrics
• Hidden symmetries and Lie algebra structures from geometric and supergravity Killing spinors
• On Conserved Quantities for the Free Motion of Particles with Spin
• Geometry, conformal Killing-Yano tensors and conserved "currents"
• On the characterization of infinitesimal symmetries of the relativistic phase space
• Integrability Conditions for Killing-Yano Tensors and Maximally Symmetric Spaces in the Presence of Torsion
• Massless geodesics in $Ad{S}_5\times Y(p,q)$ as a superintegrable system
• TCFHs, hidden symmetries and type II theories
• Higher-dimensional lifts of Killing-Yano forms with torsion
• A Class of Integrable Metrics and Gauge Fields
• TCFHs, hidden symmetries and M-theory backgrounds
• A Class of Integrable Metrics II
• Ricci-flat metrics on the cone over ${\mathbb{CP}}^2\#\overline{{\mathbb{CP}}^2}$
• TCFHs, IIB warped AdS backgrounds and hidden symmetries
• Killing Spinors and Related Symmetries in Six Dimensions
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations