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

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

2007-02-26

arxiv.org/abs/math/0702790v3

Mathematics

Differential Geometry

18 pages, The main formula has been corrected

Scientific paper

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.

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