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Parallel spinors and connections with skew-symmetric torsion in string theory
We describe all almost contact metric, almost hermitian and G2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection.Expand
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On the Spinor Representation of Surfaces in Euclidean 3-Space. ∗
The aim of the present paper is to clarify the relationship between immersions of surfaces and solutions of the Dirac equation. The main idea leading to the description of a surface M2 by a spinorExpand
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Weak $Spin(9)$-Structures on 16-dimensional Riemannian Manifolds
The aim of the present paper is the investigation of $Spin(9)$-structures on 16-dimensional manifolds from the point of view of topology as well as holonomy theory. First we construct severalExpand
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Spinorial description of SU(3) - and G 2 -manifolds
Abstract We present a uniform description of SU ( 3 ) -structures in dimension 6 as well as G 2 -structures in dimension 7 in terms of a characterising spinor and the spinorial field equations itExpand
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Killing spinor equations in dimension 7 and geometry of integrable G2-manifolds
Abstract We compute the scalar curvature of seven-dimensional G 2 -manifolds admitting a G 2 -connection with totally skew-symmetric torsion. We prove the formula for the general solution of theExpand
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On the holonomy of connections with skew-symmetric torsion
We investigate the holonomy group of a linear metric connection with skew-symmetric torsion. In case of the euclidian space and a constant torsion form this group is always semisimple. It does notExpand
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G2-manifolds with parallel characteristic torsion
Abstract We classify 7-dimensional cocalibrated G 2 -manifolds with parallel characteristic torsion and non-abelian holonomy. All these spaces admit a metric connection ∇ c with totallyExpand
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The Einstein-Dirac Equation on Riemannian Spin Manifolds
Abstract We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational field with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purposeExpand
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Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors
Abstract We generalize the well-known lower estimates for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold proved by Friedrich [Math. Nachr. 97 (1980) 117–146] andExpand
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On types of non-integrable geometries
We study the types of non-integrable $\mathrm{G}$-structures on Riemannian manifolds. In particular, geometric types admitting a connection with totally skew-symmetric torsion are characterized.Expand
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