Related papers: Complex Balanced Spaces
This paper defines coherent manifolds and discusses their properties and their application in quantum mechanics. Every coherent manifold with a large group of symmetries gives rise to a Hilbert space, the completed quantum space of $Z$,…
Let G be a unimodular Lie group, X a compact manifold with boundary, and M the total space of a principal bundle G--> M-->X so that M is also a strongly pseudoconvex complex manifold. In this work, we show that if there exists a point p in…
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…
We show that the deformation space of complex parallelisable nilmanifolds can be described by polynomial equations but is almost never smooth. This is remarkable since these manifolds have trivial canonical bundle and are holomorphic…
A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.
We discuss our recent results on the existence and classification problem of complex and Kaehler structures on compact solvmanifolds. In particular, we determine in this paper all the complex surfaces which are diffeomorphic to compact…
We characterise the existence of balanced and pluriclosed metrics on compact quotients of real semisimple Lie groups equipped with regular complex structures, in terms of Vogan diagrams. Consequently, such complex manifolds cannot…
Manin's conjecture predicts an asymptotic formula for the number of rational points of bounded height on a smooth projective variety in terms of its global geometric invariants. The strongest form of the conjecture implies certain…
We study the structure of warped compactifications of type IIB string theory to six space-time dimensions. We find that the most general four-manifold describing the internal dimensions is conformal to a Kahler manifold, in contrast with…
We first notice in this article that if a compact K\"{a}hler manifold has the same integral cohomology ring and Pontrjagin classes as the complex projective space $\mathbb{C}P^n$, then it is biholomorphic to $\mathbb{C}P^n$ provided $n$ is…
In this paper, firstly, we mainly study the relationship of balanced pairs among three Abelian categories in a recollement. As an application of admissible balanced pairs, we introduce the notion of the relative tilting modules, and give a…
We study many properties concerning weak K\"ahlerianity on compact complex manifolds which admits a holomorphic submersion onto a K\"ahler or a balanced manifold. We get generalizations of some results of Harvey and Lawson (the K\"ahler…
We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces.…
We describe the mirror of the Z orbifold as a representation of a class of generalized Calabi-Yau manifolds that can be realized as manifolds of dimension five and seven. Despite their dimension these correspond to superconformal theories…
We study the existence of three classes of Hermitian metrics on certain types of compact complex manifolds. More precisely, we consider balanced, SKT and astheno-K\"ahler metrics. We prove that the twistor spaces of compact hyperk\"ahler…
The moduli space of N=1 type II warped compactions to flat space with generic internal fluxes is studied. Using the underlying integrable generalized complex structure that characterizes these vacua, the different deformations are…
The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional structure which generalizes the notion of…
We study higher complex Sobolev spaces and their corresponding functional capacities. In particular, we prove the Moser-Trudinger inequality for these spaces and discuss some relationships between these spaces and the complex…
We consider (compact or noncompact) Lorentzian manifolds whose holonomy group has compact closure. Among other results, we obtain that this property is equivalent to admitting a parallel timelike vector field. We also derive some properties…
In this paper, we construct tools from the holomorphic twistor spaces that we introduced in \cite{Gindi1} to derive results about the complex geometries of their base manifolds. In particular, we develop a new approach to studying…