Related papers: Holomorphic Lagrangian fibrations on hypercomplex …

We study parabolic automorphisms of irreducible holomorphically symplectic manifolds with a lagrangian fibration. Such automorphisms are (possibly up to taking a power) fiberwise translations on smooth fibers, and their orbits in a general…

We give an equivalent definition of compact locally conformally hyperk\"ahler manifolds in terms of the existence of a nondegenerate complex two-form with natural properties. This is a conformal analogue of Beauville's theorem stating that…

Let $M$ be a hyperkahler manifold of maximal holonomy (that is, an IHS manifold), and let $K$ be its Kahler cone, which is an open, convex subset in the space $H^{1,1}(M, R)$ of real (1,1)-forms. This space is equipped with a canonical…

On a complex manifold an Hermitian metric which is simultaneously SKT and balanced has to be necessarily K\"ahler. It has been conjectured that if a compact complex manifold (M,J) has an SKT metric and a balanced metric both compatible with…

We extend the Abreu-Guillemin theory of invariant K\"ahler metrics from toric symplectic manifolds to any symplectic manifold admitting a toric action of a symplectic torus bundle. We show that these are precisely the symplectic manifolds…

It is demonstrated that when the bundle of 2-forms on a four-dimensional manifold M admits an almost-complex structure any choice of "real + imaginary" subspace decomposition of the bundle defines a conjugation map, as well as a Hermitian…

We prove that every irreducible component of a fibre of a complex Lagrangian fibration is Lagrangian subvariety. Especially, complex Lagrangian fibations are equidimensional.

We give a general construction of extremal Kaehler metrics on the total space of certain holomorphic submersions, extending results of Dervan-Sektnan, Fine, and Hong. We consider submersions whose fibres admit a degeneration to Kaehler…

By virtue of the well-known theorem, a structure Lie group K of a principal bundle $P$ is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/K. In gauge theory, such sections are treated as Higgs…

We present a new simple proof of the fact that certain group manifolds as well as certain homogeneous spaces G/H of dimension 4n admit a quaternionic triple of integrable complex structures that are covariantly constant with respect to the…

In this paper we study the homogeneous Kaehler manifolds (h.K.m.) which can be Kaehler immersed into finite or infinite dimensional complex space forms. On one hand we completely classify the h.K.m. which can be Kaehler immersed into a…

Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong…

We introduce the notion of a Hyper-K\"{a}hler manifold $X$ induced by a Hodge structure of K3-type. We explore this notion for the known deformation types of hyper-K\"{a}hler manifolds studying those that are induced by a K3 or abelian…

Totally complex submanifolds of a quaternionic K\"{a}hler manifold are analogous to complex submanifolds of a K\"{a}hler manifold. In this paper, we construct an example of a non-compact totally complex submanifold of maximal dimension of a…

We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kaehler manifold X. These solutions are known to be related to polystable triples via a Kobayashi-Hitchin type…

For a general cubic fourfold, it was observed by Donagi and Markman that the relative intermediate Jacobian fibration associated to the family of its hyperplane sections carries a natural holomorphic symplectic form making the fibration…

We show that on an HKT manifold the holonomy of the Obata connection is contained in SL(n,H) if and only if the Lee form is an exact one form. As an application, we show compact HKT manifolds with holomorphically trivial canonical bundle…

In this article we study complex properties of minimal Lagrangian submanifolds in Kaehler ambient spaces, and how they depend on the ambient curvature. In particular, we prove that, in the negative curvature case, minimal Lagrangians do not…

A local classification of the Hermitian manifolds with flat associated connection is given. Hermitian manifolds admitting locally a conformal metric with flat associated connection are characterized by a curvature identity. Locally…

We give a new construction of strict deformation quantization of symplectic manifolds equipped with a proper Lagrangian fiber bundle structure, whose representation spaces are the quantum Hilbert spaces obtained by geometric quantization.…