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

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

2003-02-28

arxiv.org/abs/math/0302358v2

Mathematics

Differential Geometry

11 pages, LaTeX

Scientific paper

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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