Please use this identifier to cite or link to this item: http://prr.hec.gov.pk/jspui/handle/123456789/2466
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dc.contributor.authorAli, Danish-
dc.date.accessioned2017-12-14T05:19:34Z-
dc.date.available2017-12-14T05:19:34Z-
dc.date.issued2009-
dc.identifier.uri http://prr.hec.gov.pk/jspui/handle/123456789//2466-
dc.description.abstractIn the present thesis we investigate the almost Hermitian geometry of the twistor spaces of oriented Riemannian 4-manifolds. Holomorphic and orthogonal bisectional curvatures have been intensively explored on K ̈hler manifolds and a lot of important results have been obtained in this case. a But in the non-K ̈hler case these curvatures are not very well studied and it seems a that the main reason for that is the lack of interesting examples. The first part of the thesis is devoted to the study of the curvature properties of Atiyah-Hitchin- Singer and Eells-Salamon almost Hermitian structures. This is used to provide some interesting examples of almost Hermitian 6-manifolds of constant or strictly positive holomorphic, Hermitian and orthogonal bisectional curvatures. In the second part of the thesis we determine the Gray-Hervella classes of the so-called compatible almost Hermitian structures on the twistor spaces, recently in- troduced by G. Deschamps . The interest in determining these classes is motivated by the fact that the Gray-Hervella classification is a very useful tool in studying almost complex manifolds. Our results in this direction generalize the well known integrabil- ity theorems by Atiyah-Hitchin-Singer, Eells-Salamon and Deschamps and show that there is a close relation between the properties of the spectrum of the anti-self-dual Weyl tensor of an almost K ̈hler 4-manifold and the almost Hermitian geometry of a its twistor space.en_US
dc.description.sponsorshipHigher Education Commission, Pakistanen_US
dc.language.isoenen_US
dc.subjectNatural Sciencesen_US
dc.subjectMathematicsen_US
dc.subjectGeneral principles of mathematicsen_US
dc.subjectAlgebraen_US
dc.titleHERMITIAN GEOMETRY OF TWISTOR SPACESen_US
dc.typeThesisen_US
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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