Torsion of SU(2)-structures and Ricci curvature in dimension 5
Lucio Bedulli, Luigi Vezzoni
Abstract
In anlogy with the work of R. Bryant on the Ricci tensor of a G2-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 α-Einstein condition forces some special SU(2)-structures to be Sasaki-Einstein.
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