2001/11/30 by Thomas Friedrich, Stefan Ivanov
Mathematics · Physics and Astronomy · #math.DG #hep-th #msc:53C25 #msc:53C27 #msc:53C55 #msc:81T30
published as J. Reine Ang. Math. 559 (2003), 217-236 · Latex2e, 15 pages; Final version of the paper, the preliminary title has been "Almost contact manifolds and type II equations"
arxiv created 2003/09/29 · arxiv updated 2009/11/30
We classify locally homogeneous quasi-Sasakian manifolds in dimension five that admit a parallel spinor ψ of algebraic type F ⋅ ψ= 0 with respect to the unique connection ∇ 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.