Related papers: K\"ahler submanifolds of the symmetrized polydisc

In this paper, we provide a sufficient condition on the non-existence of the common K\"ahler submanifolds between the complex Euclidean space and the ball bundles of some Hermitian vector bundles over K\"ahler manifolds. Then we get the…

In this article we study isometric immersions of nearly K\"ahler manifolds into a space form (specially Euclidean space) and show that every nearly K\"ahler submanifold of a space form has a totally umbilic foliation whose leafs are…

In this article, we investigate the K\"ahler immersions of special Asymptotically Locally Euclidean (ALE) K\"ahler metrics into complex space forms. We provide a relation between K\"ahler immersions problem of these metrics and the sign of…

Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat K\"ahler metrics on a minimal K\"ahler surface whose K\"ahler classes stay in a compact…

Let $M$ be a compact K\"ahler manifold and $N$ be a subvariety with codimension greater than or equal to 2. We show that there are no complete K\"ahler--Einstein metrics on $M-N$. As an application, let $E$ be an exceptional divisor of $M$.…

Minimal isometric immersions F in codimension two from a complete Kahler manifold into Euclidean space had been classified for dimension greater than or equal to 3. In this note we describe the non--minimal situation by showing that, if F…

The aim of this paper is to prove that there exists no cohomogeneity one $G-$invariant proper biharmonic hypersurface into the Euclidean space ${\mathbb R}^n$, where $G$ denotes a tranformation group which acts on ${\mathbb R}^n$ by…

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…

We introduce and study the notion of atomic sheaves and complexes on higher-dimensional hyper-K\"ahler manifolds and show that they share many of the intriguing properties of simple sheaves on K3 surfaces. For example, we prove formality of…

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…

We show that asymptotically Schwarzschildean 3-manifolds cannot contain minimal surfaces obtained by perturbative deformations of a Euclidean catenoid, no matter how small the ADM mass of the ambient space and how large the neck of the…

We proved a conjecture of D. Freed that there are no non-trivial complete special Kaehler manifolds.

We follow our study of non-K\"ahler complex structures on $R^4$ that we defined in a previous paper. We prove that these complex surfaces do not admit any smooth complex compactification. Moreover, we give an explicit description of their…

It is proved some results about existence and non existence of unit normal sections of submanifolds of the Euclidean space and sphere which associated Gauss maps are harmonic. Some applications to CMC hypersurfaces of the sphere and…

We introduce the class of almost symmetric submanifolds of Euclidean space, a close relative of symmetric submanifolds and (contact) sub-Riemannian symmetric spaces. More specifically, we prove that every full irreducible almost symmetric…

We completely describe inhomogeneous properly embedded almost symmetric submanifolds of Euclidean space as certain unions of parallel symmetric submanifolds of the ambient Euclidean space.

In this note we show that on any compact subdomain of a K\"ahler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to the linearized…

We prove that there are no minimal hypersurfaces properly immersed in any region of the Euclidean space bounded by unstable minimal cones. We also prove the analogous result for $r$-minimal hypersurfaces.

In this note we prove a nonexistence result for proper biharmonic maps from complete non-compact Riemannian manifolds of dimension \(m=\dim M\geq 3\) with infinite volume that admit an Euclidean type Sobolev inequality into general…

Totally complex submanifolds of a quaternionic K\"{a}hler manifold are analogous to complex submanifolds of a K\"{a}hler manifold. In this paper, we construct an example of a non-compact totally complex submanifold of maximal dimension of a…