Asian Research Thesis Index

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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