scholarly journals On some compact almost Kähler locally symmetric space

Author(s):  
Takashi Oguro

In the framework of studying the integrability of almost Kähler manifolds, we prove that if a compact almost Kähler locally symmetric spaceMis a weakly ,∗-Einstein vnanifold with non-negative ,∗-scalar curvature, thenMis a Kähler manifold.

1993 ◽  
Vol 08 (39) ◽  
pp. 3773-3784 ◽  
Author(s):  
S. AOYAMA ◽  
S. VANDOREN

We show that the Kähler structure can be naturally incorporated in the Batalin-Vilkovisky formalism. The phase space of the BV formalism becomes a fermionic Kähler manifold. By introducing an isometry we explicitly construct the fermionic irreducible hermitian symmetric space. We then give some solutions of the master equation in the BV formalism.


2006 ◽  
Vol 17 (01) ◽  
pp. 35-43 ◽  
Author(s):  
MARCO BRUNELLA

We prove that the canonical bundle of a foliation by curves on a compact Kähler manifold is pseudoeffective, unless the foliation is a (special) foliation by rational curves.


Author(s):  
Stefan Schreieder

Abstract A conjecture of Kotschick predicts that a compact Kähler manifold $X$ fibres smoothly over the circle if and only if it admits a holomorphic one-form without zeros. In this paper we develop an approach to this conjecture and verify it in dimension two. In a joint paper with Hao [ 10], we use our approach to prove Kotschick’s conjecture for smooth projective three-folds.


2017 ◽  
Vol 4 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Michela Zedda

Abstract In this paper we study Kähler manifolds that are strongly not relative to any projective Kähler manifold, i.e. those Kähler manifolds that do not share a Kähler submanifold with any projective Kähler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results which highlight some relations between this property and the existence of a full Kähler immersion into the infinite dimensional complex projective space. As application we get that the 1-parameter families of Bergman-Hartogs and Fock-Bargmann-Hartogs domains are strongly not relative to projective Kähler manifolds.


2016 ◽  
Vol 08 (04) ◽  
pp. 589-626 ◽  
Author(s):  
Michael Entov ◽  
Misha Verbitsky

Let [Formula: see text] be a closed symplectic manifold of volume [Formula: see text]. We say that the symplectic packings of [Formula: see text] by balls are unobstructed if any collection of disjoint symplectic balls (of possibly different radii) of total volume less than [Formula: see text] admits a symplectic embedding to [Formula: see text]. In 1994, McDuff and Polterovich proved that symplectic packings of Kähler manifolds by balls can be characterized in terms of the Kähler cones of their blow-ups. When [Formula: see text] is a Kähler manifold which is not a union of its proper subvarieties (such a manifold is called Campana simple), these Kähler cones can be described explicitly using the Demailly and Paun structure theorem. We prove that for any Campana simple Kähler manifold, as well as for any manifold which is a limit of Campana simple manifolds in a smooth deformation, the symplectic packings by balls are unobstructed. This is used to show that the symplectic packings by balls of all even-dimensional tori equipped with Kähler symplectic forms and of all hyper-Kähler manifolds of maximal holonomy are unobstructed. This generalizes a previous result by Latschev–McDuff–Schlenk. We also consider symplectic packings by other shapes and show, using Ratner’s orbit closure theorem, that any even-dimensional torus equipped with a Kähler form whose cohomology class is not proportional to a rational one admits a full symplectic packing by any number of equal polydisks (and, in particular, by any number of equal cubes).


1995 ◽  
Vol 18 (2) ◽  
pp. 331-340
Author(s):  
M. Hasan shahid ◽  
A. Sharfuddin

The study ofCR-submanifolds of a Kähler manifold was initiated by Bejancu [1]. Since then many papers have appeared onCR-submanifolds of a Kähler manifold. Also, it has been studied that generic submanifolds of Kähler manifolds [2] are generalisations of holomorphic submanifolds, totally real submanifolds andCR-submanifolds of Kähler manifolds. On the other hand, many examplesC2of generic surfaces in which are notCR-submanifolds have been given by Chen [3] and this leads to the present paper where we obtain some necessary conditions for a generic submanifolds in a locally conformal Kähler manifold with four canonical strucrures, denoted byP,F,tandf, to have parallelP,Fandt. We also prove that for a generic submanifold of a locally conformal Kähler manifold,Fis parallel ifftis parallel.


Author(s):  
Masaya Kawamura

We introduce Kähler-like, G-Kähler-like almost Hermitian metrics. We characterize the Kähler-likeness and the G-Kähler-likeness, and show that these properties are equivalent on nearly Kähler manifolds. Furthermore, we prove that a nearly Kähler manifold with the Kähler-likeness is Kähler.


2014 ◽  
Vol 150 (11) ◽  
pp. 1869-1902 ◽  
Author(s):  
Junyan Cao

AbstractLet $X$ be a compact Kähler manifold and let $(L,{\it\varphi})$ be a pseudo-effective line bundle on $X$. We first define a notion of numerical dimension for pseudo-effective line bundles with singular metrics, and then discuss the properties of this numerical dimension. Finally, we prove a very general Kawamata–Viehweg–Nadel-type vanishing theorem on an arbitrary compact Kähler manifold.


1989 ◽  
Vol 114 ◽  
pp. 77-122 ◽  
Author(s):  
Josef Dorfmeister

In 1967 Gindikin and Vinberg stated the Fundamental Conjecture for homogeneous Kähler manifolds. It (roughly) states that every homogeneous Kähler manifold is a fiber space over a bounded homogeneous domain for which the fibers are a product of a flat with a simply connected compact homogeneous Kähler manifold. This conjecture has been proven in a number of cases (see [6] for a recent survey). In particular, it holds if the homogeneous Kähler manifold admits a reductive or an arbitrary solvable transitive group of automorphisms [5]. It is thus tempting to think about the general case. It is natural to expect that lack of knowledge about the radical of a transitive group G of automorphisms of a homogeneous Kähler manifold M is the main obstruction to a proof of the Fundamental Conjecture for M. Thus it is of importance to consider the Kähler algebra generated by the radical of the Lie algebra of G. Computations in this context suggest that one rather considers Kähler algebras generated by an arbitrary solvable ideal.


Author(s):  
Hans-Joachim Hein ◽  
Rareş Răsdeaconu ◽  
Ioana Şuvaina

Abstract The underlying complex structure of an ALE Kähler manifold is exhibited as a resolution of a deformation of an isolated quotient singularity. As a consequence, there exist only finitely many diffeomorphism types of minimal ALE Kähler surfaces with a given group at infinity.


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