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 mathematical background of this type ofâ€¦ (More)

A geometric classiication of the compact four-dimensional Einstein-Weyl manifolds with at least four-dimensional symmetry group is given. Our results also sharpen previous results on four-dimensionalâ€¦ (More)

We present the extended Kuranishi space for Kodaira surface as a nontrivial example to Kontsevich and Barannikovâ€™s extended deformation theory. We provide a non-trivial example of Hertling-Maninâ€™sâ€¦ (More)

Let M = Î“\G be a nilmanifold endowed with an invariant complex structure. We prove that Kuranishi deformations of abelian complex structures are all invariant complex structures, generalizing aâ€¦ (More)

It is proved that if the twistor space of a self-dual four-manifold of positive scalar curvature contains a real effective divisor of degree two, then the four-manifold is difFeomorphic to theâ€¦ (More)

We develop deformation theory for abelian invariant complex structures on a nilmanifold, and prove that in this case the invariance property is preserved by the Kuranishi process. A purely algebraicâ€¦ (More)

If M is a quaternionic manifold and P is an S-instanton over M , then Joyce constructed a hypercomplex manifold we call P(M) over M . These hypercomplex manifolds admit a U(2)-action of a specialâ€¦ (More)

Due to a recent theorem of Taubes, self-dual conformal structures on compact four-dimensional manifolds exist in abundance [43]. Therefore, finding examples in general is no longer an issue in thisâ€¦ (More)

We find sufficient conditions for principal toric bundles over compact KÃ¤hler manifolds to admit Calabi-Yau connections with torsion, as well as conditions to admit strong KÃ¤hler connections withâ€¦ (More)

This article provides a complete description of the differential Gerstenhaber algebras of all nilpotent complex structures on any real six-dimensional nilpotent algebra. As an application, weâ€¦ (More)