Almost contact manifolds, connections with torsion and parallel spinors

Details Almost contact manifolds, connections with torsion and parallel spinors Almost contact manifolds, connections with torsion and parallel spinors

2001-11-12

arxiv.org/abs/math/0111131v2

J. Reine Ang. Math. 559 (2003), 217-236

Mathematics

Differential Geometry

Latex2e, 15 pages; Final version of the paper, the preliminary title has been "Almost contact manifolds and type II equations"

Scientific paper

We classify locally homogeneous quasi-Sasakian manifolds in dimension five that admit a parallel spinor $\psi$ of algebraic type $F \cdot \psi = 0$ with respect to the unique connection $\nabla$ preserving the quasi-Sasakian structure and with totally skew-symmetric torsion. We introduce a certain conformal transformation of almost contact metric manifolds and discuss a link between them and the dilation function in 5-dimensional string theory. We find natural conditions implying conformal invariances of parallel spinors. We present topological obstructions to the existence of parallel spinors in the compact case.

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