Related papers: Surfaces on Oeljeklaus-Toma Manifolds

If one could assume that local coordinates in a Riemannian manifold were orthogonal, then local expressions for differential operators, and curvature computations, would be simplified. It is always possible on 2-manifolds, using geometric…

A 2-torus manifold is a closed connected smooth n-manifold with a non-free effective smooth $\mathbb{Z}^n_2$-action. In this paper, we prove that a 2-torus manifold is equivariantly formal if and only if the $\mathbb{Z}^n_2$-action is…

The Leit-Faden of the article (which is partially a survey) is a negative answer to the question whether, for a compact complex manifold which is a $K(\pi, 1)$ the diffeomorphism type determines the deformation type. We show that a…

Using min-max theory, we show that in any closed Riemannian manifold of dimension at least 3 and at most 7, there exist infinitely many smoothly embedded closed minimal hypersurfaces. It proves a conjecture of S.-T. Yau. This paper builds…

This paper contains some results about Teichm\"uller spaces of non-orientable surfaces (Klein surfaces). We prove several theorems giving isomorphisms between deformation spaces of Klein surfaces. These results show the similarity between…

It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as…

In this short note, as a simple application of the strong result proved recently by B\"ohm and Wilking, we give a classification on closed manifolds with 2-nonnegative curvature operator. Moreover, by the new invariant cone constructions of…

We introduce and study a special class of Kato manifolds, which we call toric Kato manifolds. Their construction stems from toric geometry, as their universal covers are open subsets of toric algebraic varieties of non-finite type. This…

Iwasawa manifold is a compact complex homogeneous manifold isomorphic to a quotient of the group of complex unipotent $3 \times 3$ matrices by a cocompact lattice. We prove that any compact complex curve in an Iwasawa manifold is contained…

Let $(M^n, g)$ be a compact K\"ahler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact K\"ahler manifold $N^k$ with $c_1 < 0$. This confirms a…

We determine the Hodge endomorphism algebras of non-projective complex K3 surfaces (and more generally, hyperk\"ahler manifolds). We show that they are either totally real fields or number fields generated by Salem numbers. This is unlike…

We introduce and study Hodge-de Rham numbers for compact almost complex 4-manifolds, generalizing the Hodge numbers of a complex surface. The main properties of these numbers in the case of complex surfaces are extended to this more general…

Two questions on the topology of compact energy surfaces of natural two degrees of freedom Hamiltonian systems in a magnetic field are discussed. We show that the topology of this 3-manifold (if it is not a unit tangent bundle) is uniquely…

Symplectic forms taming complex structures on compact manifolds are strictly related to Hermitian metrics having the fundamental form $\partial \bar \partial $-closed, i.e. to strong K\"ahler with torsion (${\rm SKT}$) metrics. It is still…

We prove that under certain conditions on the mean curvature and on the Kaehler angles, a compact submanifold M of real dimension 2n, immersed into a Kaehler-Einstein manifold N of complex dimension 2n, must be either a complex or a…

The twistor space of a Riemannian 4-manifold carries two almost complex structures, $J_+$ and $J_-$, and a natural closed 2-form $\omega$. This article studies limits of manifolds for which $\omega$ tames either $J_+$ or $J_-$. This amounts…

We review some cohomological aspects of complex and hypercomplex manifolds and underline the differences between both realms. Furthermore, we try to highlight the similarities between compact complex surfaces on one hand and compact…

For each member of an infinite family of homology classes in the K3-surface E(2), we construct infinitely many non-isotopic symplectic tori representing this homology class. This family has an infinite subset of primitive classes. We also…

We define secondary theories and characteristic classes for simplicial smooth manifolds generalizing Karoubi's multiplicative K-theory and multiplicative cohomology groups for smooth manifolds. As a special case we get versions of the…

We observed in our previous paper that all the complex structures on four-dimensional compact solvmanifolds, including tori, are left-invariant. In this paper we will give an example of a six-dimensional compact solvmanifold which admits a…