Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 8 (2012), 058, 15 pages      arXiv:1205.6036      http://dx.doi.org/10.3842/SIGMA.2012.058
Contribution to the Special Issue “Geometrical Methods in Mathematical Physics”

Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits

Mihai Visinescu a and Eduard Vîlcu b, c
a) National Institute for Physics and Nuclear Engineering, Department of Theoretical Physics, P.O. Box M.G.-6, Magurele, Bucharest, Romania
b) Petroleum-Gas University of Ploieşti, Department of Mathematical Economics, Bulevardul Bucureşti, Nr. 39, Ploieşti 100680, Romania
c) University of Bucharest, Faculty of Mathematics and Computer Science, Research Center in Geometry, Topology and Algebra, Str. Academiei, Nr. 14, Sector 1, Bucharest 70109, Romania

Received May 29, 2012, in final form July 23, 2012; Published online August 27, 2012

Abstract
The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new Killing forms on Einstein-Sasaki manifolds are identified associated with the complex volume form of the cone manifolds. Finally the Killing forms on mixed 3-Sasaki manifolds are briefly described.

Key words: Killing forms; Einstein-Sasaki space; Calabi-Yau spaces.

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