### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 077, 28 pages      math.DG/0611288      https://doi.org/10.3842/SIGMA.2006.077

### The Torsion of Spinor Connections and Related Structures

University of Dortmund, 44221 Dortmund, Germany

Received August 25, 2006, in final form November 03, 2006; Published online November 09, 2006

Abstract
In this text we introduce the torsion of spinor connections. In terms of the torsion we give conditions on a spinor connection to produce Killing vector fields. We relate the Bianchi type identities for the torsion of spinor connections with Jacobi identities for vector fields on supermanifolds. Furthermore, we discuss applications of this notion of torsion.

Key words: spinor connection; torsion; Killing vector; supermanifold.

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