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Spin(9)-structures and connections with totally skew-symmetric torsion. (English) Zbl 1039.53049

The problem studied in this paper originates in the type II string theory where the basic model consists of a Riemannian metric, a metric connection with totally skew-symmetric torsion, and also of a dilation function and a spinor field. The author is interested in metric connections with totally skew-symmetric torsion, establishes a criterion for existence of such a connection on a 16-dimensional Riemannian manifold with Spin(9)-structure and shows that if this criterion holds then such a connection is unique. Therewith he characterizes geometric types admitting such connections and, in particular, demonstrates that in difference with some other structures (i.e., \(G_2\)-, Spin(7)-, quaternionic Kähler and contact structures) for Spin(9)-structures the existence of a connection with totally skew-symmetric torsion is not invariant under conformal changes of a metric.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
53C05 Connections (general theory)
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References:

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