Torsion of SU(2)-structures and Ricci curvature in dimension 5

Abstract

In anlogy with the work of R. Bryant on the Ricci tensor of a G${}_2$-structure, we study the intrinsic torsion of an SU$(2)$-structure on a 5-dimensional manifold deriving an explicit expression for the Ricci and the scalar curvature in terms of torsion forms and its derivative. As a consequence of this formula we prove that the $\alpha$-Einstein condition forces some special SU(2)-structures to be Sasaki-Einstein.

18 pages, The main formula has been corrected

References in corpus (2)

• The Ricci tensor of SU(3)-manifolds
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds

Cited by in corpus (1)

• Killing-Yano tensors and some applications