Special riemannian metrics and kaehler geometry

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The aim of this proposal is the study of special Riemannian metrics from the point of view of  Kahler geometry. Such metrics appear as mathematical objects of physical models arising in General Relativity and String Theory, but also in the algebro-geometric notion of stability of projective varities. I plan to work on the following specific problems: 1. Existence of extremal Kahler metrics on projective bundles.  This project would provide a fertile testing ground for the conjectures relating extremal Kahler metrics to stability of projective varities. 2. Extension of the notion of  a Hamiltonian 2-form to the contex of Sasakian geometry. This would give a systematic approach to some new constructions of Sasaki-Einstein metrics found by string theorists. 3. Generalized Kahler metrics. The concept of a generalized complex structure has been introduced by Hitchin to provide a natural differential geometric framework for some notions of current interest in string theory. My project here aims at classifying a certain  type of generalized Kahler manifolds.