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Hermitian Geometry of Twistor Spaces

Thesis Info

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Author

Danish Ali

Supervisor

Oleg Mushkarov

Program

PhD

Country

Pakistan

Thesis Completing Year

2009

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2466/1/2557S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726368844

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In 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.
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نبوت ، اقتدائے مصطفیٰؐ ہے


نبوّت ، اقتدائے مصطفیؐ ہے
صحابہؓ میں ولائے مصطفیؐ ہے

عبادت گر جسے کہتے ہیں سجدہ
سوئے کعبہ ؛ ادائے مصطفیؐ ہے

جہاں پر انتہا روح الامیںؑ کی
وہاں سے ابتدائے مصطفیؐ ہے

جہالت ، تیرگی ، بے رہروی ہے
اگر کچھ ماسوائے مصطفیؐ ہے

لحد میں انشا اللہ ہم کہیں گے
خدا اپنا خدائے مصطفیؐ ہے

’’رمیت اذ رمیت‘‘ کا خلاصہ
ادائے رب ، ادائے مصطفیؐ ہے

عمرؓ کو عظمتیں جس نے عطا کیں
فقط حرفِ دعائے مصطفیؐ ہے

A Diasporic Study of Cultural Identity in Ayad Akhtar’s Disgraced and American Dervish

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