All Theses and Dissertations

Degree

Master of Science in Mathematics

Department

Department of Mathematical Sciences

Date of Award

Fall 2015

Advisor

Dr. Danish Ali

Committee Member 1

Dr. Mobeen Munir, University of Education, Lahore

Committee Member 2

Dr. Najma Abdul Rehman, COMSAT Institute of Information Technology, Sahiwal

Committee Member 3

Dr. Junaid Alam Khan, Institute of Business Administration, Karachi

Project Type

Thesis

Access Type

Restricted Access

Pages

vi, 43

Abstract

The idea of Twistor Theory was created by English Physicist R. Penrose, is that the geometry of a conformal manifold M can be encoded in holomorphic terms of the so-called Twistor Spaces associated to M. The negative twistor space of an oriented Riemannian 4-manifold M , is a two-sphere bundle L whose fiber at any point m of M consists of all complex structure on tangent space Tm M compatible with metric and the opposite orientation of M. The Smooth Manifold L admits two almost complex structure J1 and J2 introduced by Atiyah-Hitchin-Singer and Elles-Salamon respectively, recently G. De- schamp observed that given a smooth map f from L to L ,a fibre preserving map, one can define an almost complex structure Jf on twistor space L and J1, J2 are the special cases of Jf . J. Davidov and O. Mushkarov studied the existence of holomorphic function with respect to almost complex structure J1 and J2. I have rigorously explore this existence in this thesis also I concluded that the existence of holomorphic function with respect to compatible almost complex structure Jf can be proven in the same way.

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