相关论文: Indefinite locally conformal Kaehler manifolds

We will discuss in this paper homogeneous locally conformally Keahler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey…

Some curvature properties of Kahler manifolds of indefinite metrics are studied. Analogues of a Kulkarni's theorem are proved for such manifolds.

We present an overview of recent results in locally conformally K\"ahler geometry, with focus on the topological properties which obstruct the existence of such structures on compact manifolds.

We study complex non-K\"ahler manifolds with Hermitian metrics being locally conformal to metrics with special cohomological properties. In particular, we provide examples where the existence of locally conformal holomorphic-tamed…

The purpose of the present paper is to study the differential geometric properties of a quaternion CR-submanifold in a locally conformal quaternion Kaehler manifold.

I present a selection of results on locally conformally K\"ahler geometry published after 1997. The proofs are mainly sketched, some of them are even omitted. Several open problems are indicated in the end.

We investigate isometric immersions of locally conformally Kaehler metrics into Hopf manifolds. In particular, we study Hopf-induced metrics on compact complex surfaces.

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…

Indefinite Kaehler solutions of the Einstein equations are studied, and it is almost completely determined which compact complex surfaces admit such metrics.

In this article we develop a new approach to the problem of the stability of locally conformally K\"ahler structures (l.c.k structures) under small deformations of complex structures and deformations of flat line bundles. We show that under…

We prove that any Kaehler manifold admitting a flat complex conformal connection is a Bochner-Kaehler manifold with special scalar distribution and zero geometric constants. Applying the local structural theorem for such manifolds we obtain…

We classify and investigate locally conformally K\"ahler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on…

We study integral geometric properties of non-compact harmonic spaces.

We present a compared analysis of some properties of indefinite almost $\mathcal{S}$-manifolds and indefinite $\mathcal{S}$-manifolds. We give some characterizations in terms of the Levi-Civita connection and of the characteristic vector…

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 basic class of the non-integrable almost complex manifolds with Norden metric is considered. Its curvature properties are studied. The isotropic Kaehler type of investigated manifolds is introduced and characterized geometrically.

This is a final step in a local classification of pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric.

It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field)…

We describe special Ka\"hler geometry, special quaternionic manifolds, and very special real manifolds and analyze the structure of their isometries. The classification of the homogeneous manifolds of these types is presented.

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…