Related papers: Complex foliations and Kahler QCH surfaces
In this article we introduce the notion of Polyhedral Kahler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and…
Starting with a concise review of quaternionic geometry and quaternionic K{\"a}hler manifolds, we define a transversely quaternionic K{\"a}hler foliation. Then we formulate and prove the foliated versions of the now classical results of…
We introduce a class of objects which we call 'affine surfaces'. These provide families of foliations on surfaces whose dynamics we are interested in. We present and analyze a couple of examples, and we define concepts related to these in…
We review how a reduction procedure along a principal fibration and an unfolding procedure associated to a suitable momentum map allow to describe the K\"ahler geometry of a finite dimensional complex projective spaces.
Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one has explicit control over the curvature tensor, we completely classify such…
The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…
We present existence results for certain singular 2-dimensional foliations on 4-manifolds. The singularities can be chosen to be simple, e.g. the same as those that appear in Lefschetz pencils. There seems to be a wealth of such creatures…
A way to characterize the space of leaves of a foliation in terms of connections is proposed. A particular example of vertex algebra cohomology of codimension one foliations on complex curves is considered.
The aim of this work is to give a twistor presentation of recent results about bi-Hermitian metrics on compact complex surfaces with odd first Betti number.
We study the space of deformations of a smooth foliation of the 5-sphere by complex manifolds
The aim of this paper is to present the first examples of compact, simply connected holomorphically pseudosymmetric Kahler manifolds.
In this paper, complex Hessian equation over K\"ahler manifold was studied. Under the condition that the underline K\"ahler manifold has non-negative holomorphic bisectional curvature, the existence and regularity of the solution was…
In this survey we discuss the problem of the existence of rational curves on complex surfaces, both in the K\"ahler and non-K\"ahler setup. We systematically go through the Enriques--Kodaira classification of complex surfaces to highlight…
In this paper, we study the properties of coverings of locally conformally K\"ahler (LCK) spaces with singularities. We begin by proving that a space is LCK if any only if its universal cover is K\"ahler, thereby generalizing a result from…
The aim of this paper is to describe Kahler surfaces which admit an opposite almost Hermitian structure satisfying the first Gray condition
The paper contains a description of the links of complex surface germ.
We give a method for constructing Kummer covers with many points over finite fields.
We present an explicit formula for the deformation quantization on K\"{a}hler manifolds.
In this paper we give new examples of QCH Kahler surfaces whose opposite almost Hermitian strucure is Hermitian and not locally conformally Kahler. In this way we give also a large class of examples of Hermitian surfaces with J-invariant…
In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.