Almost contact manifolds, connections with torsion and parallel spinors

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We classify locally homogeneous quasi-Sasakian manifolds in dimension five that admit a parallel spinor $ψ$ of algebraic type $F \cdot ψ= 0$ 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.
Latex2e, 15 pages; Final version of the paper, the preliminary title has been "Almost contact manifolds and type II equations"

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Differential Geometry, High Energy Physics - Theory, 53C25, 53C27, 53C55, 81T30

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http://salesiana.dossiersoluciones.com/handle/123456789/62626

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0111131
 http://arxiv.org/abs/math/0111131
 J. Reine Ang. Math. 559 (2003), 217-236

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arXiv