Generalised $G_2$-manifolds

Details Generalised $G_2$-manifolds Generalised $G_2$-manifolds

2004-11-29

arxiv.org/abs/math/0411642v4

Commun.Math.Phys. 265 (2006) 275-303

Mathematics

Differential Geometry

27 pages. v2: references added. v3: wrong argument (Theorem 3.3) and example (Section 4.1) removed, further examples added, no

Scientific paper

10.1007/s00220-006-0011-7

We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. The unconstrained critical points generalise the notion of a manifold of holonomy $G_2$, while the constrained ones give rise to a new geometry without a classical counterpart. We characterise these structures by the means of spinors and show the integrability conditions to be equivalent to the supersymmetry equations on spinors in supergravity theory of type IIA/B with bosonic background fields. In particular, this geometry can be described by two linear metric connections with skew torsion. Finally, we construct explicit examples by using the device of T-duality.

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