相关论文: A detailed description of the generalized Calabi t…

In this paper we give classification of K\"ahler surfaces of generalized Calabi type.

The aim of this paper is to describe Kahler surfaces with quasi-constant holomorphic curvature

In this paper we describe QCH K\"ahler surfaces $(M,g,J)$ of generalized orthotoric type. We introduce a distinguished orthonormal frame on $(M,g)$ and give the structure equations for $(M,g,J)$. In the case when $I$ is conformally K\"ahler…

In this paper we prove that some well known K\"ahler surfaces with zero scalar curvature are QCH K\"ahler. We prove that family of generalized Taub-Nut K\"ahler surfaces parametrized by $k\in[-1,1]$ is of orthotoric type for $k\in(-1,1)$…

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…

In this paper, we construct metallic K\"ahler and nearly metallic K\"ahler structures on Riemanian manifolds. For such manifolds with these structures, we study curvature properties. Also we describe linear connections on the manifold,…

The aim of this paper is to describe complex foliations on Kahler surfaces.

The aim of this paper is to classify compact Kahler manifolds with quasi-constant holomorphic sectional curvature.

Polyhedral K\"ahler surfaces are a class of complex surfaces, which are flat everywhere except on a two-dimensional skeleton. They are defined as a generalisation of the "gluing a polygon side by side" construction of flat Riemann surfaces.…

Let (M,J) be a minimal compact complex surface of Kaehler type. It is shown that the smooth 4-manifold M admits a Riemannian metric of positive scalar curvature iff (M,J) admits a KAEHLER metric of positive scalar curvature. This extends…

We present new constructions of Kaehler metrics with constant scalar curvature on complex surfaces, in particular on certain del Pezzo surfaces. Some higher dimensional examples are provided as well.

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the…

In this manuscript we study natural symmetries of Kaehler manifolds: constant holomorphic sectional curvature Kaheler manifolds, semisymmetric Kaehler manifolds and holomorphically pseudosymmetric Kaehler manifolds. We get characterization…

The space $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ admits a natural homogeneous pseudo-Riemannian nearly Kaehler structure. We investigate almost complex surfaces in this space. In particular we obtain a complete classification of the…

Generalized Calabi-Gray manifolds are non-K\"ahler complex manifolds with very explicit geometry yet not being homogeneous. In this note, we demonstrate that how generalized Calabi-Gray manifolds can be used to answer some questions in…

We continue to develop our method for effectively computating the special K\"ahler geometry on the moduli space of Calabi-Yau manifolds. We generalize it to all polynomial deformations of Fermat hypersurfaces.

We construct the first examples of non-K\"ahler complex structures on $R^4$. These complex surfaces have some analogies with the complex structures constructed in early Fifties by Calabi and Eckmann on the products of two odd-dimensional…

We study the K\"ahler geometry of stage n Bott manifolds, which can be viewed as $n$-dimensional generalizations of Hirzebruch surfaces. We show, using a simple induction argument and the generalized Calabi construction from…

A contact hypersurface in a Kaehler manifold is a real hypersurface for which the induced almost contact metric structure determines a contact structure. We carry out a systematic study of contact hypersurfaces in Kaehler manifolds. We then…

This article finds constant scalar curvature Kahler metrics on certain compact complex surfaces. The surfaces considered are those admitting a holomorphic submersion to a curve, with fibres of genus at least 2. The proof is via an adiabatic…