Related papers: Higher dimensional generalizations of twistor spac…

It is very well known that Hopf real hypersurfaces in the complex projective space can be locally characterized as tubes over complex submanifolds. This also holds true for some, but not all, Hopf real hypersurfaces in the complex…

Given a compact complex $n$-fold $X$ satisfying the $\partial\bar\partial$-lemma and supposed to have a trivial canonical bundle $K_X$ and to admit a balanced (=semi-K\"ahler) Hermitian metric $\omega$, we introduce the concept of…

We construct a family of $6$-dimensional compact manifolds $M(A)$, which are simultaneously diffeomorphic to complex Calabi-Yau manifolds and symplectic Calabi-Yau manifolds. They have fundamental groups $\mathbb{Z} \oplus \mathbb{Z}$,…

We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…

Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one has explicit control over the curvature tensor, we completely classify such…

The main goal of our paper is the study of several classes of submanifolds of generalized complex manifolds. Along with the generalized complex submanifolds defined by Gualtieri and Hitchin (we call these ``generalized Lagrangian…

In this paper we propose a generalization of the extension complexity of a polyhedron $Q$. On the one hand it is general enough so that all problems in $P$ can be formulated as linear programs with polynomial size extension complexity. On…

In this note we begin a systematic study of compact conformal manifolds of SCFTs in four dimensions (our notion of compactness is with respect to the topology induced by the Zamolodchikov metric). Supersymmetry guarantees that such…

In this paper, we generalize the construction of Deligne-Hitchin twistor space by gluing two certain Hodge moduli spaces. We investigate such generalized Deligne-Hitchin twistor space as a complex analytic manifold. More precisely, we show…

We recently constructed examples of compact Kaeler manifolds which do not have the homotopy type of a projective complex manifold. They were however obtained by blowing-up certain complex tori, which are themselves deformation equivalent to…

We study topological strings on non-commutative resolutions of singular Calabi-Yau threefolds that are double covers of $\mathbb{P}^3$, ramified over determinantal octic surfaces. Using conifold transitions to complete intersections in…

We prove that if a Calabi--Yau manifold $M$ admits a holomorphic Cartan geometry, then $M$ is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on compact K\"ahler manifolds. We also…

Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong…

In this paper we describe a physical realization of a family of non-compact Kahler threefolds with trivial canonical bundle in hybrid Landau-Ginzburg models, motivated by some recent non-Kahler solutions of Strominger systems, and utilizing…

Let H be a 4 dimensional almost Hermitian manifold which satisfies the Kaehler identity. Then H is complex Osserman if and only if H has constant holomorphic sectional curvature. We also classify in arbitrary dimensions all the complex…

We investigate compact Kahler manifolds, which are acted on by a semisimple compact Lie group G of isometries with one hypersurface orbit. In case of ordinary action and projectable complex structure, we set up a one to one correspondence…

We find geometric conditions on a Hermitian-Weyl manifold under which the complex structure is a pseudo-harmonic map in the sense of G. Kokarev \cite{K09} from the manifold into its twistor space. This is done under the assumption that the…

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 propose a class of N=2 supersymmetric nonlinear sigma models on the noncompact Ricci-flat Kahler manifolds, interpreted as the complex line bundles over the hermitian symmetric spaces. Kahler potentials and Ricci-flat metrics for these…

A twist construction for manifolds with torus action is described generalising certain T-duality examples and constructions in hypercomplex geometry. It is applied to complex, SKT, hypercomplex and HKT manifolds to construct compact…