Mathematics – Differential Geometry
Scientific paper
2005-02-21
Mathematics
Differential Geometry
examined DPhil Thesis, University of Oxford, 2004 v2: Proposition 3.5 and Theorem 3.6 fixed
Scientific paper
The primary aim of this thesis is to investigate metrics which are induced by a differential form and arise as a critical point of Hitchin's variational principle. Firstly, we investigate metrics associated with the structure group PSU(3) acting in its adjoint representation. We derive various obstructions to the existence of a topological reduction to PSU(3). For compact manifolds, we also find sufficient conditions if the PSU(3)-structure lifts to an SU(3)-structure. We give a Riemannian characterisation of topological PSU(3)-structures through an invariant spinor valued 1-form and show that the PSU(3)-structure is integrable if and only if the spinor valued 1-form defines a co-closed Rarita-Schwinger field. Moreover, we construct non-symmetric (compact) examples. Secondly, we consider even or odd forms which can be naturally interpreted as spinors for a spin structure on $T\oplus T^*$. As such, the forms we consider induce a reduction from $Spin(7,7)$ to $G_2\times G_2$. We give a topological classification of $G_2\times G_2$-structures. We prove that the condition for being a critical point is equivalent to the supersymmetry equations on spinors in supergravity theory of type IIA/B with NS-NS background fields. Examples are systematically constructed by the device of T-duality.
No associations
LandOfFree
Special metric structures and closed forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Special metric structures and closed forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Special metric structures and closed forms will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-197718