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 …

In recent years quaternionic Kahler and hyperkähler manifolds have received a great deal of
attention. They appear in many different areas of mathematics and mathematical physics. It …

Abstract We investigate N= 2, D= 5 supersymmetry and matter-coupled supergravity theories
in a superconformal context. In a first stage we do not require the existence of a lagrangian …

The internal space of a N= 4 supersymmetric model with Wess–Zumino term has a
connection with totally skew-symmetric torsion and holonomy in SP (n). We study the …

This review article intends to introduce the reader to non-integrable geometric structures on
Riemannian manifolds and invariant metric connections with torsion, and to discuss recent …

The holonomy of the Bismut connection on Vaisman manifolds is studied. We prove that if M
2 n is endowed with a Vaisman structure, then the holonomy group of the Bismut connection …

Let M be a hypercomplex Hermitian manifold,(M, I) the same manifold considered as a
complex Hermitian with a complex structure I induced by the quaternions. The standard …

A twist construction for manifolds with torus action is described generalizing certain T-duality
examples and constructions in hypercomplex geometry. It is applied to complex, SKT …

In this paper, we give a classification of all compact Hermitian manifolds with flat Bismut
connection. We show that the torsion tensor of such a manifold must be parallel, thus the …