The Ricci tensor of SU(3)-manifolds

Details The Ricci tensor of SU(3)-manifolds The Ricci tensor of SU(3)-manifolds

2006-06-30

arxiv.org/abs/math/0606786v3

J. Geom. Phys. 57 (2007), n. 4, 1125--1146

Mathematics

Differential Geometry

25 pages. To appear in "Journal of Geometry and Physics". Corollary 4.1 is modified. Some typos are corrected

Scientific paper

10.1016/j.geomphys.2006.09.007

Following the approach of Bryant we study the intrinsic torsion of a
SU(3)-manifold deriving a number of formulae for the Ricci and the scalar
curvature in terms of torsion forms. As a consequence we prove that in some
special cases the Einstein condition forces the vanishing of the intrinsic
torsion.

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