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

Lucio Bedulli; Luigi Vezzoni

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arXiv · math/0702790

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

Lucio Bedulli·Luigi Vezzoni

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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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Lucio Bedulli, Luigi Vezzoni. 2007-02-26. Torsion of SU(2)-structures and Ricci curvature in dimension 5. https://arxiv.org/abs/math/0702790

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