相关论文: Symplectically aspherical manifolds

In this paper, we introduce a new kind of Siegel upper half space and consider the symplectic geometry on it explicitly under the action of the group of all holomorphic transformations of it. The results and methods will form a basis for…

The main theorem of this paper is a result of estimated transversality with respect to stratifications of jet spaces in the approximately holomorphic category over an almost-complex manifold. The notion of asymptotic ampleness of complex…

We study symplectic structures on four-dimensional small covers. Our main result shows that every symplectic four-dimensional small cover is aspherical. We then classify symplectic small covers over products of two polygons, proving that…

We exhibit many examples of closed symplectic manifolds on which there is an autonomous Hamiltonian whose associated flow has no nonconstant periodic orbits (the only previous explicit example in the literature was the torus T^2n (n\geq 2)…

This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to…

A prequantization bundle is a negative circle bundle over a symplectic surface together with a contact form induced by a S1-invariant connection. Given a symplectically aspherical symplectic filling of a prequantization bundle satisfying…

This is an overview article on selected topics in symplectic geometry written for the Handbook of Differential Geometry (volume 2, edited by F.J.E. Dillen and L.C.A. Verstraelen).

We consider the homotopy type of maps between symplectic surface whose graphs form symplectic submanifolds of the product. We give a purely topological model for this space in terms of maps with constrained numbers of pre-images. We use…

We study constructions of contact forms on closed manifolds. A notion of strong symplectic fold structure is defined and we prove that there is a contact form on $M \x X$ provided that $M$ admits such a structure and $X$ is contact. This…

We show, in this note, that on any symplectic supermanifold, even or odd, there exist an infinite dimensional affine space of symmetric connections, compatible to the symplectic form.

In this article we study covering spaces of symplectic toric orbifolds and symplectic toric orbifold bundles. In particular, we show that all symplectic toric orbifold coverings are quotients of some symplectic toric orbifold by a finite…

This survey explores the geometry of three-dimensional Anosov flows from the perspective of contact and symplectic geometry, following the work of Mitsumatsu, Eliashberg-Thurston, Hozoori, and the author. We also present a few original…

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…

In the paper there are described new examples of conformally flat three dimensional almost cosymplectic manifolds. All these manifolds form a class which was completely characterized.

We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.

We give a survey of the theory of affine spheres, emphasizing the convex cases and relationsships to Monge-Ampere equations and geometric structures on manifolds.

In this paper we survey some recent works that take the first steps toward establishing bilateral connections between symplectic geometry and several other fields, namely, asymptotic geometric analysis, classical convex geometry, and the…

This is a survey on bi-Lagrangian manifolds, which are symplectic manifolds endowed with two transversal Lagrangian foliations. We also study the non-integrable case (i.e., a symplectic manifold endowed with two transversal Lagrangian…

In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.

This is an exposition of the Donaldson geometric flow on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The original work appeared in [1].