Related papers: Compact Conformal Manifolds
We give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the…
In this paper we survey $n$-dimensional solenoidal manifolds for $n=1,2$ and 3, and present new results about them. Solenoidal manifolds of dimension $n$ are metric spaces locally modeled on the product of a Cantor set and an open…
We classify ${\cal N}=1$ gauge theories with simple gauge groups in four dimensions which possess a conformal manifold passing through weak coupling. A very rich variety of models is found once one allows for arbitrary representations under…
We construct two new versions of the c-map which allow us to obtain the target manifolds of hypermultiplets in Euclidean theories with rigid N =2 supersymmetry. While the Minkowskian para-c-map is obtained by dimensional reduction of the…
Using an effective field theory approach and the language of SU(N)-structures, we study higher derivative corrections to the supersymmetry constraints for compactifications of string or M-theory to Minkowski space. Our analysis is done…
We consider a class of smooth oriented Lorentzian manifolds in dimensions three and four which admit a nowhere vanishing conformal Killing vector and a closed two-form that is invariant under the Lie algebra of conformal Killing vectors.…
We show that the standard definitions of Sasaki structures have elegant and simplifying interpretations in terms of projective differential geometry. For Sasaki-Einstein structures we use projective geometry to provide a resolution of such…
Using the theory of totally real number fields we construct a new class of compact complex non-K{\"a}hler manifolds in every even complex dimension and study their analytic and geometric properties.
We study biharmonic maps between conformally compact manifolds, a large class of complete manifolds with bounded geometry, asymptotically negative curvature, and smooth compactification. These metrics provide a far-reaching generalization…
We present new definitions for and give a comprehensive treatment of the canonical compactification of configuration spaces due to Fulton-MacPherson and Axelrod-Singer in the setting of smooth manifolds, as well as a simplicial variant of…
For each compact almost Kahler manifold $(X,\om,J)$ and an element A of $H_2(X;Z)$, we describe a closed subspace $\ov{\frak M}_{1,k}^0(X,A;J)$ of the moduli space $\ov{\frak M}_{1,k}(X,A;J)$ of stable J-holomorphic genus-one maps such that…
We give four constructions of non-$\partial\bar\partial$ (hence non-K\"ahler) manifolds: (1) A simply connected page-$1$-$\partial\bar\partial$-manifold (2) A simply connected $dd^c+3$-manifold (3) For any $r\geq 2$, a simply connected…
We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products…
This article investigates the subject of rigid compact complex manifolds. First of all we investigate the different notions of rigidity (local rigidity, global rigidity, infinitesimal rigidity, etale rigidity and strong rigidity) and the…
A curve, that is, a connected, reduced, projective scheme of dimension 1 over an algebraically closed field, admits two types of compactifications of its (generalized) Jacobian: the moduli schemes of P-quasistable torsion-free, rank-1…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
The characterization of a six- (or seven)-dimensional internal manifold with metric as having positive, zero or negative curvature is expected to be an important aspect of warped compactifications in supergravity. In this context, Douglas…
In this note we prove that a four-dimensional compact oriented half-confor\-mally flat Riemannian manifold $M^4$ is topologically $\mathbb{S}^{4}$ or $\mathbb{C}\mathbb{P}^{2},$ provided that the sectional curvatures all lie in the interval…
We construct a compact convex generating set $\mathcal{C}_n$ of the moduli set of closed connected projective special real manifolds of fixed dimension $n$. We show that a closed connected projective special real manifold corresponds to an…
In this article we introduce the notion of Polyhedral Kahler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces, and…