On some properties of the manifolds with skew-symmetric torsion and holonomy SU(n) and Sp(n)

2003/02/28 by Anna Fino, Fino, Anna, Gueo Grantcharov +1
Mathematics · Physics and Astronomy · #17B30 #53C26 #53C55 #81T30 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.DG #msc:17B30 #msc:53C26 #msc:53C55 #msc:81T30

paper · pdf · doi:10.48550/arxiv.math/0302358

11 pages, LaTeX

arxiv created 2003/06/19 · arxiv updated 2009/11/30

Abstract

In this paper we provide examples of hypercomplex manifolds which do not carry HKT structure. We also prove that the existence of HKT structure is not stable under small deformations. Similarly we provide examples of compact complex manifolds with vanishing first Chern class which do not admit a Hermitian structure with restricted holonomy of its Bismut connection in SU(n). Again we prove that such property is not stable under small deformations.

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