Special metric structures and closed forms

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dc.creatorWitt, Frederik
dc.date2005-02-21
dc.date2006-02-21
dc.date.accessioned2026-07-07T06:39:28Z
dc.date.available2026-07-07T06:39:28Z
dc.descriptionThe 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.
dc.descriptionexamined DPhil Thesis, University of Oxford, 2004 v2: Proposition 3.5 and Theorem 3.6 fixed
dc.identifierhttps://arxiv.org/abs/math/0502443
dc.identifierhttp://arxiv.org/abs/math/0502443
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101088
dc.subjectDifferential Geometry
dc.subjectHigh Energy Physics - Theory
dc.subject53C10; 53C25; 58E15; 83E30; 83E50
dc.titleSpecial metric structures and closed forms
dc.typetext

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