منابع مشابه
Twistor spaces for HKT manifolds
We construct the twistor space associated with an HKT manifold, that is, a hyper-Kähler manifold with torsion, a type of geometry that arises as the target space geometry in two-dimensional sigma models with (4,0) supersymmetry. We show that this twistor space has a natural complex structure and is a holomorphic fibre bundle over the complex projective line with fibre the associated HKT manifol...
متن کاملBalanced HKT metrics and strong HKT metrics on hypercomplex manifolds
A manifold (M, I, J,K) is called hypercomplex if I, J,K are complex structures satisfying quaternionic relations. A quaternionic Hermitian hypercomplex manifold is called HKT (hyperkähler with torsion) if the (2,0)-form Ω associated with the corresponding Sp(n)-structure satisfies ∂Ω = 0. A Hermitian metric ω on a complex manifold is called balanced if d∗ω = 0. We show that balanced HKT metrics...
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We study M-theory on G2 holonomy spaces that are constructed by dividing a seven-torus by some discrete symmetry group. We classify possible group elements that may be used in this construction and use them to find a set of possible orbifold groups that lead to co-dimension four singularities. We describe how to blow up such singularities, and then derive the moduli Kähler potential for M-theor...
متن کاملFinsler manifolds with non-Reimannian holonomy
The aim of this paper is to show that the holonomy group of a non-Riemannian Finsler manifold of constant curvature with dimension n > 2 cannot be a compact Lie group and hence it cannot occur as the holonomy group of any Riemannian manifold. This result gives a positive answer to the following problem formulated by S. S. Chern and Z. Shen: Is there a Finsler manifold whose holonomy group is no...
متن کاملFinsler manifolds with non-Riemannian holonomy
The aim of this paper is to show that holonomy properties of Finsler manifolds can be very different from those of Riemannian manifolds. We prove that the holonomy group of a positive definite non-Riemannian Finsler manifold of non-zero constant curvature with dimension > 2 cannot be a compact Lie group. Hence this holonomy group does not occur as the holonomy group of any Riemannian manifold. ...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2011
ISSN: 1687-0247,1073-7928
DOI: 10.1093/imrn/rnr160