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Torsion of SU(2)-structures and Ricci curvature in dimension 5
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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.
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AdS$_3$ solutions in Massive IIA with small $\mathcal{N}=(4,0)$ supersymmetry
Two new classes of AdS3 x S2 solutions in massive IIA with small N=(4,0) supersymmetry are derived, along with their T-dual IIB counterparts.
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