A generalized Fourier transform is defined on any Riemannian manifold that satisfies a Parseval-Plancherel theorem and constructs unique momentum-space labels by resolving degeneracy with fiberwise maximal Abelian commuting sets from geometric symmetries.
Killing-Yano tensors and some applications
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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.
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The mixed Einstein equations in stationary-axisymmetric geometries with absent mixed fluxes enforce a constant-Schwarzian constraint whose global-regularity branch is precisely the Kerr sector.
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Generalized Fourier Transforms for Momentum-Space Construction on Riemannian Manifolds
A generalized Fourier transform is defined on any Riemannian manifold that satisfies a Parseval-Plancherel theorem and constructs unique momentum-space labels by resolving degeneracy with fiberwise maximal Abelian commuting sets from geometric symmetries.
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Local Origin of Hidden Symmetry in Rotating Spacetimes
The mixed Einstein equations in stationary-axisymmetric geometries with absent mixed fluxes enforce a constant-Schwarzian constraint whose global-regularity branch is precisely the Kerr sector.