Show simple item record

dc.contributor.advisorSeshadri, Harish
dc.contributor.authorGururaja, H A
dc.date.accessioned2014-09-03T05:54:21Z
dc.date.accessioned2018-07-31T06:09:02Z
dc.date.available2014-09-03T05:54:21Z
dc.date.available2018-07-31T06:09:02Z
dc.date.issued2014-09-03
dc.date.submitted2011
dc.identifier.urihttps://etd.iisc.ac.in/handle/2005/2376
dc.identifier.abstracthttp://etd.iisc.ac.in/static/etd/abstracts/3059/G25112-Abs.pdfen_US
dc.description.abstractThis thesis consists of two parts. In the first part, we study certain Ricci flow invariant nonnegative curvature conditions as given by B. Wilking. We begin by proving that any such nonnegative curvature implies nonnegative isotropic curvature in the Riemannian case and nonnegative orthogonal bisectional curvature in the K¨ahler case. For any closed AdSO(n,C) invariant subset S so(n, C) we consider the notion of positive curvature on S, which we call positive S- curvature. We show that the class of all such subsets can be naturally divided into two subclasses: The first subclass consists of those sets S for which the following holds: If two Riemannian manifolds have positive S- curvature then their connected sum also admits a Riemannian metric of positive S- curvature. The other subclass consists of those sets for which the normalized Ricci flow on a closed Riemannian manifold with positive S-curvature converges to a metric of constant positive sectional curvature. In the second part of the thesis, we study the behavior of Ricci flow for a manifold having positive S - curvature, where S is in the first subclass. More specifically, we study the Ricci flow for a special class of metrics on Sp+1 x S1 , p ≥ 4, which have positive isotropic curvature.en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesG25112en_US
dc.subjectRicci Flowen_US
dc.subjectRiemannian Manifoldsen_US
dc.subjectManifolds (Mathematics)en_US
dc.subjectCurvatureen_US
dc.subjectIsotropic Curvatureen_US
dc.subjectS−curvatureen_US
dc.subject.classificationGeometryen_US
dc.titleRicci Flow And Isotropic Curvatureen_US
dc.typeThesisen_US
dc.degree.namePhDen_US
dc.degree.levelDoctoralen_US
dc.degree.disciplineFaculty of Scienceen_US


Files in this item

This item appears in the following Collection(s)

Show simple item record