When Comes such Another? Asma Jahangir 1952 –2018

On the 11th of February this year death vanquished Pakistan’s Asma Jahangir: Nothing else could. Her name will endure; yet one cannot go on to say “death thou art dead” for the vacuum in the field where this indomitable and intellectually gifted lawyer fought and won her battles for the forgotten and ignored, the resource-less, and – above all – for the politically and socially persecuted is felt more gravely with each passing day: Asma Jahangir was a convinced human rights activist. There are many such, but she was a uniquely effective and successful one.

Hermitian Geometry of Twistor Spaces

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.