Related papers: Exotic geometric structures on Kodaira surfaces

We show that automorphism groups of Hopf and Kodaira surfaces have unbounded finite subgroups. For elliptic fibrations on Hopf, Kodaira, bielliptic, and K3 surfaces, we make some observations on finite groups acting along the fibers and on…

In 1995, S. Adams and G. Stuck as well as A. Zeghib independently provided a classification of non-compact Lie groups which can act isometrically and locally effectively on compact Lorentzian manifolds. In the case that the corresponding…

This paper is devoted to characterizing complex projective structures defined on Riemann surface orbifolds and giving rise to injective developing maps defined on the monodromy covering of the surface (orbifold) in question. The relevance…

A Lie hypersurface in the complex hyperbolic space is a homogeneous real hypersurface without focal submanifolds. The set of all Lie hypersurfaces in the complex hyperbolic space is bijective to a closed interval, which gives a deformation…

Using group actions and orbit-stabilizer methods, we study the geometry of isomorphism classes of finite-dimensional $\omega$-Lie algebras over a field $\mathbb{K}$ of characteristic $\neq 2$ and establish a one-to-one correspondence…

We prove that the only complex parabolic geometries on Calabi-Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact K\"ahler manifolds.

We classify commutative algebraic monoid structures on normal affine surfaces over an algebraically closed field of characteristic zero. The answer is given in two languages: comultiplications and Cox coordinates. The result follows from a…

We show that if a compact complex surface admits a locally conformally flat metric, then it cannot contain a smooth rational curve of odd self-intersection. In particular, the surface has to be minimal. Then we give a list of possibilities…

A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve, such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant rational cohomology in…

In this paper we classify all singular irreducible symplectic surfaces, i.e., compact, connected complex surfaces with canonical singularities that have a holomorphic symplectic form $\sigma$ on the smooth locus, and for which every finite…

Let $X$ be surface with isolated singularities in the complex projective space $P^3$ and let denote $Y$ the smooth part of $X$. In this note we discuss some aspects of the topology of such quasi-projective surfaces $Y$: the fundamental…

We characterize isometric actions on compact Kaehler manifolds admitting a Lagrangian orbit, describing under which condition the Lagrangian orbit is unique. We furthermore give the complete classification of simple groups acting on the…

We prove that the deRham cohomology classes of Lee forms of locally conformally symplectic structures taming the complex structure of a compact complex surface $S$ with first Betti number equal to $1$ is either a non-empty open subset of…

In this paper we give the topological classification of real primary Kodaira surfaces and we describe in detail the structure of the corresponding moduli space. One of the main tools is the orbifold fundamental group of a real variety. Our…

Inspired by a recent result of Levine-Lidman-Piccirillo, we construct infinitely many exotic smooth structures on some closed four-manifolds with definite intersection form and fundamental group isomorphic to $\Z /2\Z$. Similar…

We give a geometric characterization of certain hypersurfaces of cohomogeneity one in the complex projective and hyperbolic planes. We also obtain some partial classifications of austere hypersurfaces and of Levi-flat hypersurfaces with…

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…

We study surfaces constructed from groups of units in quaternion orders $\Lambda$ over the integers in real quadratic fields k. A short presentation of some general theory of such surfaces is given, in particular, we construct certain…

Motivated by analogous results in locally conformal symplectic geometry, we study different classes of G$_2$-structures defined by a locally conformal closed 3-form. In particular, we give a complete characterization of invariant exact…

We examine functorial and homotopy properties of the exotic characteristic homomorphism in the category of Lie algebroids which was lastly obtained by the authors in [4]. This homomorphism depends on a triple (A,B,$\nabla$) where B…