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Almost contact manifolds, connections with torsion, and parallel spinors. (English) Zbl 1035.53058

This is a continuation of a previous paper of the authors [Asian J. Math. 6, 303–336 (2002; Zbl 1127.53304)], in which they consider the classification of 5-dimensional locally homogeneous quasi-Sasakian manifolds which admit a particular type of parallel spinor. They introduce a special conformal transformation of almost contact metric manifolds and establish a link between them and the dilation function in 5-dimensional string theory of type II. This is shown to lead to natural conditions which imply the conformal invariance of parallel spinors, and in the compact case they exhibit topological obstructions to the existence of parallel spinors.
Contents includes: an introduction; contact connections with parallel spinors; normal almost contact metric structures with \(\nabla\)-parallel spinors; the quasi-Sasakian case; the dilation function and conformal transformations; and harmonic 1-forms in the presence of \(\nabla\)-parallel spinors.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C27 Spin and Spin\({}^c\) geometry
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
53D15 Almost contact and almost symplectic manifolds

Citations:

Zbl 1127.53304
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References:

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