Parallel spinors and connections with skew-symmetric torsion in string theory. (English) Zbl 1127.53304

Friedrich, Thomas; Ivanov, Stefan

Asian J. Math. 6, No. 2, 303-335 (2002).

We describe all almost contact metric, almost Hermitian and \(G_2\)-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the \(\nabla\)-parallel spinors. In particular, we obtain partial solutions of the type II string equations in dimensions \(n = 5\), 6 and 7.

MSC:

53C27	Spin and Spin\({}^c\) geometry
58J60	Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
53C05	Connections (general theory)
53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords:

\(G_2\)-structures; skew-symmetric torsion tensor; parallel spinors; type II string equations