相关论文: Manifold structures for sets of solutions of the g…

We construct solutions of the vacuum vector constraint equations on manifolds with cylindrical ends.

We construct a natural generalized complex structure on the total space of any bundle endowed with a Chern connection and whose typical fibre is a homogeneous symplectic manifold. This extends known constructions of generalized complex…

Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven…

In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…

We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of…

We study generalized complex cohomologies of generalized complex structures constructed from certain symplectic fibre bundles over complex manifolds. We apply our results in the case of left-invariant generalized complex structures on…

The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion…

In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact…

A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…

We study the notion of geometric structures for toposes: This generalizes the notion of (X,G) manifolds. We give some applications to algebraic geometry

We study values of generalized polylogarithms at various points and relationships among them. Polylogarithms of small weight at the points 1/2 and -1 are completely investigated. We formulate a conjecture about the structure of the linear…

Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains…

A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…

We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.

We discuss various algebraic quantum structures associated to monotone Lagrangian submanifolds and we present a number of applications, computations and examples.

An introduction to the applications of algebraic surgery to the structure theory of high-dimensional topological manifolds.

Given a collection of N asymptotically Euclidean ends with zero scalar curvature, we construct a Riemannian manifold with zero scalar curvature and one asymptotically Euclidean end, whose boundary has a neighborhood isometric to the…

In this note, we describe a procedure to construct generalized complex structures with an arbitrarily large number of type change loci on products of the circle with a connected sum of closed 3-manifolds. The loci need not be isotopic.

We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are…

In this paper, we prove that the set of solutions of constraint equations for coupled Einstein and scalar fields in classical general relativity possesses Hilbert manifold structure. We follow the work of R. Bartnik [2] and use weighted…