2005/02/21 by Frederik Witt, Witt, Frederik · 2 citations
Mathematics · #53C10 #53C25 #58E15 #83E30 #83E50 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0502443
openalex publication_date 2005/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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⊕ T^*. As such, the forms we consider induce a reduction from Spin(7,7) to G2× G2. We give a topological classification of G2× G2-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.