Theses and Dissertations

Student Number

11641

Degree

Master of Science in Mathematics

Department

Department of Computer Science

Date of Award

Spring 2020

Advisor

Dr. Danish Ali

Committee Member 1

Dr. Absar-ul-Haq, Institute of Business Administration, Karachi

Committee Member 2

Dr. Najma Abdul Rehman, Institute of Business Administration, Karachi

Committee Member 3

Dr. Hisham Bin Zubair, Institute of Business Administration, Karachi

Project Type

Thesis

Access Type

Restricted Access

Document Version

Final

Pages

vii, 54

Subjects

Geometry

Abstract

Twistor Space was first described by Roger Penrose and Malcolm MacCallum in the 1960s. Let (N, h) be an oriented Riemannian 4-manifold" then twistor space of (N, h) is the two-sphere subbundle W of A~T N which has an l-parameter family of Riemannian metric gr. The Ricci curvature of (W, gt) was defined in [9]. In [6], G. Deschamps defined almost complex (a.c) structures 3j on a manifold W of dimension 6 under a fiber preserving morphism j: W ---7 W of the bundle W such that n 0 j = Jr. The Ricci tensor of the twistor space of an almost Hermitian Riemannian 4-manifold was also discussed w.r.t an a.c structure. defined with the help of the morphism j: W ---7 Wand a sectionj3 E A2T N in [10] which is a particular case of the arbitrary morphism f. In this dissertation, I studied the Ricci tensor of (W, gt) and the conditions in which the Ricci tensor of twistor space with almost Hermitian base manifold is also Hermitian correspond to the a.c structure 5. Furthermore, we can also explore the conditions for the Ricci tensor of (W, gt) to be Hermitian corresponding to the complex structure 3) defined under an arbitrary fiber preserving map from the twistor space W to W. Tags from this library: No tags from this library for this title.

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