To Antonio Naveira on the occasion of his 60th birthday We analyse the relationship between the components of the intrinsic torsion of an SU (3)-structure on a 6-manifold and a G 2-structure on aâ€¦ (More)

We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5-manifolds defined by a generalized Killing spinor. We proveâ€¦ (More)

This paper classifies Hermitian structures on 6-dimensional nilmanifolds M = Î“\G for which the fundamental 2-form is âˆ‚âˆ‚-closed, a condition that is shown to depend only on the underlying complexâ€¦ (More)

A study is made of real Lie algebras admitting compatible complex and product structures, including numerous 4-dimensional examples. If g is a Lie algebra with such a structure then itsâ€¦ (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)

We describe topologically the discriminant locus of a smooth cubic surface in the complex projective space CP that contains 5 fibres of the projection CP âˆ’â†’ S.

We identify the space of left-invariant oriented complex structures on the complex Heisenberg group, and prove that it has the homotopy type of the disjoint union of a point and a 2-sphere.â€¦ (More)

An orthogonal complex structure on a domain in R is a complex structure which is integrable and is compatible with the Euclidean metric. This gives rise to a first order system of partialâ€¦ (More)

We investigate the geometry and topology of a standard moduli space of stable bundles on a Riemann surface, and use a generalization of the Verlinde formula to derive results on intersection pairings.

Introduction There are now many explicitly known examples of metrics with holonomy group equal to G 2 , the simplest of which admit an isometry group with orbits of codimen-sion one. A metric withâ€¦ (More)