We discuss the mathematical properties of six-dimensional non-Kähler manifolds which
occur in the context of N= 1 supersymmetric heterotic and type IIA string compactifications …

The generalized Ricci flow is a geometric evolution equation which has recently emerged
from investigations into mathematical physics, Hitchin's generalized geometry program, and …

For a given complex n-fold M we present an explicit construction of all complex (n+ 1)-folds
which are principal holomorphic T 2-fibrations over M. For physical applications we consider …

Writing long books is a laborious and impoverishing act of foolishness: expanding in five
hundred pages an idea that could be perfectly explained in a few minutes. A better …

We produce examples of generalized complex structures on manifolds by generalizing
results from symplectic and complex geometry. We produce generalized complex structures …

In this paper we provide examples of hypercomplex manifolds which do not carry HKT
structures, thus answering a question in Grantcharov and Poon (Comm. Math. Phys. 213 …

Let (J, g) be a Hermitian structure on a six-dimensional compact nilmanifold M with invariant
complex structure J and compatible metric g, which is not required to be invariant. We show …

We generalize Yau's estimates for the complex Monge-Ampère equation on compact
manifolds in the case when the background metric is no longer Kähler. We prove C^∞ a …

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 …

We study balanced Hermitian structures on almost abelian Lie algebras, ie on Lie algebras
with a codimension-one abelian ideal. In particular, we classify six-dimensional almost …