We review aspects of twistor theory, its aims and achievements spanning the last five
decades. In the twistor approach, space–time is secondary with events being derived …

The book starts with a thorough introduction to connections and holonomy groups, and to
Riemannian, complex and Kähler geometry. Then the Calabi conjecture is proved and used …

This graduate level text covers an exciting and active area of research at the crossroads of
several different fields in Mathematics and Physics. In Mathematics it involves Differential …

The main result of the paper is an existence theorem for a constant scalar curvature Kahler
metric on a toric surface, assuming the K-stability of the manifold. The proof builds on earlier …

We prove that any compact complex surface with $ c_1> 0$ admits an Einstein metric which
is conformally related to a Kähler metric. The key new ingredient is the existence of such a …

A set of canonical paraHermitian connections on an almost paraHermitian manifold is
defined. ParaHermitian version of the Apostolov–Gauduchon generalization of the Goldberg …

We showed before that self-dual electromagnetism in noncommutative (NC) space–time is
equivalent to self-dual Einstein gravity. This result implies a striking picture about gravity …

A Weyl manifold is a conformal manifold equipped with a torsion free connec-tion preserving
the conformal structure, called a Weyl connection. It is said to be Ez'nstez'n-Weyl if the …

It is well-known that any 4-dimensional hyperkähler metric with two commuting Killing fields
may be obtained explicitly, via the Gibbons-Hawking Ansatz, from a harmonic function …

This paper is concerned with the construction of special metrics on non-compact 4-manifolds
which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the …