Related papers: Embedding of LCK manifolds with potential into Hop…

Given a branched cover of manifolds, one can lift homeomorphisms along the cover to obtain a (virtual) homomorphism between mapping class groups. Following a question of Margalit-Winarski, we study the injectivity of this lifting map in the…

A quaternionic K\"ahler manifold M is called {\it positive} if it has positive scalar curvature. The main purpose of this paper is to prove several connectedness theorems for quaternionic immersions in a quaternionic K\"ahler manifold, e.g.…

In this note, we shall prove geodesic convexity of the space of K\"ahler potentials on an ALE K\"ahler manifold. This extends earlier results in the compact case proved in the fundamental work of X-X. Chen. We further prove the boundedness…

This article contains a compression of results from alg-geom/9501001, with most proofs omitted. We prove that every two points of the connected moduli space of holomorphically symplectic manifolds can be connected with so-called ``twistor…

Let $M$ be a compact, holomorphic symplectic Kaehler manifold, and $L$ a non-trivial line bundle admitting a metric of semi-positive curvature. We show that some power of $L$ is effective. This result is related to the hyperkaehler SYZ…

A compact K\"ahler manifold is shown to be simply-connected if its `symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective…

Let M be a compact locally conformal hyperkaehler manifold. We prove a version of Kodaira-Nakano vanishing theorem for M. This is used to show that M admits no holomorphic differential forms, and the cohomology of the structure sheaf…

The last years have seen striking improvements on Vaisman's question about existence of locally conformally K\"ahler (lcK) metrics on compact complex surfaces. The aim of this paper is two-fold. We review results of different authors which,…

The aim of these notes is to acquaint the reader with important objects in complex algebraic geometry: K3 surfaces and their higher-dimensional analogs, hyperk\"ahler manifolds. These manifolds are interesting from several points of view:…

We establish a new criterion for a compatible almost complex structure on a symplectic four-manifold to be integrable and hence K\"ahler. Our main theorem shows that the existence of three linearly independent closed J-anti-invariant…

This paper presents two results in the realm of conformal Kaehler submanifolds. These are conformal immersions of Kaehler manifolds into the standard flat Euclidean space. The proofs are obtained by making a rather strong use of several…

In this paper we show that space of spatial polygons in semi riemann space gives a Kahler manifold. We describe the tangent space and almost complex structure which has many computational advantages.

We discuss embedding of manifolds in the category of open books, contact manifolds and contact open books. We prove an open book version of the Haefliger--Hirsch embedding theorem by showing that every $k$-connected closed $n$-manifold…

Given a complete K\"ahler manifold $(X,\,\omega)$ with finite second Betti number, a smooth complex hypersurface $Y\subset X$ and a smooth real $d$-closed $(1,\,1)$-form $\alpha$ on $X$ with arbitrary, possibly non-rational, De Rham…

We characterize those spacetimes which admit a isometric (or conformal) embedding in some Lorentz-Minkowski space L^N. In particular, any globally hyperbolic spacetime can be isometrically embedded in L^N. This is proven by a result of its…

The paper is part of an attempt of understanding non-K\"ahler threefolds. We start by looking at compact complex non-K\"ahler threefolds with algebraic dimension two and admitting locally conformally K\"ahler metrics. Under certain…

In this paper, we prove that a compact K\"ahler manifold $X$ with pseudo-effective (resp. singular positively curved) tangent bundle admits a smooth (resp. locally constant) rationally connected fibration $\phi \colon X \to Y$ onto a finite…

The Hofer-Zehnder theorem states that almost every hypersurface in a thickening of a hypersurface $S$ in a symplectic manifold $(M,\omega)$ carries a closed characteristic provided that $S$ bounds a compact submanifold and $(M,\omega)$ has…

For real projective spaces, (a) the Euclidean immersion dimension, (b) the existence of axial maps, and (c) the topological complexity are known to be three facets of the same problem. But when it comes to embedding dimension, the classical…

Let $f\colon M^{2n}\to\R^{2n+p}$, $2\leq p\leq n-1$, be an isometric immersion of a Kaehler manifold into Euclidean space. Yan and Zheng conjectured in \cite{YZ} that if the codimension is $p\leq 11$ then, along any connected component of…