Almost contact manifolds, connections with torsion and parallel spinors

Thomas Friedrich; Stefan Ivanov

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arXiv · math/0111131

Almost contact manifolds, connections with torsion and parallel spinors

Thomas Friedrich·Stefan Ivanov

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Abstract

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.

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Thomas Friedrich, Stefan Ivanov. 2003-09-29. Almost contact manifolds, connections with torsion and parallel spinors. https://arxiv.org/abs/math/0111131

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