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Publications Influence

Parallel spinors and connections with skew-symmetric torsion in string theory

- T. Friedrich, S. Ivanov
- Mathematics, Physics
- 19 February 2001

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

290 32- PDF

On the Spinor Representation of Surfaces in Euclidean 3-Space. ∗

- T. Friedrich
- Mathematics
- 30 December 1997

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 spinor… Expand

147 11- PDF

Weak $Spin(9)$-Structures on 16-dimensional Riemannian Manifolds

- T. Friedrich
- Mathematics
- 15 December 1999

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 several… Expand

56 10- PDF

Spinorial description of SU(3) - and G 2 -manifolds

- I. Agricola, S. Chiossi, T. Friedrich, Jos Holl
- Mathematics, Physics
- 20 November 2014

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 it… Expand

27 8- PDF

Killing spinor equations in dimension 7 and geometry of integrable G2-manifolds

- T. Friedrich, S. Ivanov
- Mathematics, Physics
- 19 December 2001

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 the… Expand

110 7- PDF

On the holonomy of connections with skew-symmetric torsion

- I. Agricola, T. Friedrich
- Mathematics
- 5 May 2003

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 not… Expand

101 6- PDF

G2-manifolds with parallel characteristic torsion

- T. Friedrich
- Mathematics
- 20 April 2006

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 totally… Expand

29 5- PDF

The Einstein-Dirac Equation on Riemannian Spin Manifolds

- E. C. Kim, T. Friedrich
- Mathematics
- 17 May 1999

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 purpose… Expand

75 5- PDF

Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors

- T. Friedrich, E. C. Kim
- Mathematics
- 25 June 1999

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] and… Expand

42 5- PDF

On types of non-integrable geometries

- T. Friedrich
- Mathematics, Physics
- 14 May 2002

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

55 4- PDF