Special Killing forms on toric Sasaki-Einstein manifolds

Abstract

In this paper we study the interplay between complex coordinates on the Calabi-Yau metric cone and the special Killing forms on the toric Sasaki-Einstein manifold. In the general case we give a procedure to locally construct the special Killing forms. In the final part we exemplify the general scheme in the case of the $5-$dimensional $Y^{p,q}$ spaces, identifying the additional special Killing 2-forms which were previously obtained by the second author of the present paper, but with a different method, in [Mod. Phys. Lett. A 27 (2012) 1250217].

15 pages, version accepted for publication in Physica Scripta

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Cited by in corpus (5)

• Complete integrability of geodesic motion in Sasaki-Einstein toric $Y^{p,q}$ spaces
• Action-angle variables for geodesic motions in Sasaki-Einstein spaces $Y^{p,q}$
• Transverse Kähler-Ricci flow and deformations of the metric on the Sasaki space $T^{1,1}$
• Conformal Killing $L^2-$forms on complete Riemannian manifolds with nonpositive curvature operator
• Toric data and Killing forms on homogeneous Sasaki-Einstein manifold $T^{1,1}$