相关论文: Plane curves and contact geometry
In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…
Systems with dissipation can be described using contact geometry. We introduce the concepts of symmetries and dissipation laws for contact Hamiltonian systems and study the relation between them. This is an ongoing collaboration with Xavier…
In this paper we construct various non-trivial and non-tautological cohomology classes on compactified and uncompactified strata of curves with a differential, by using the geometry of the boundary stratification of the moduli space of…
A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form $P\times \R$ where $P$ is an exact symplectic manifold is established. The class of such contact manifolds include 1-jet spaces of…
We study curvature identities on contact metric manifolds on the geometry of the corresponding almost K\"aehler cones, and we provide applications of the derived curvature identities.
We show that for a complete complex algebraic variety the pure component of homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce…
We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex…
The splitting number of a plane irreducible curve for a Galois cover is effective to distinguish the embedded topologies of plane curves. In this paper, we define a connected number of any plane curve for a Galois cover whose branch divisor…
The theory of classical types of curves in normed planes is not strongly developed. In particular, the knowledge on existing concepts of curvatures of planar curves is widespread and not systematized in the literature. Giving a…
We study the group of automorphisms of the affine plane preserving some given curve, over any field. The group is proven to be algebraic, except in the case where the curve is a bunch of parallel lines. Moreover, a classification of the…
We use the method of homological quantum reduction to construct a deformation quantization on singular symplectic quotients in the situation, where the coefficients of the moment map define a complete intersection. Several examples are…
We study the plane automorphisms given by polynomials with certain degree decompositions.
Symmetric products of curves are important spaces for both geometers and topologists, and increasingly useful objects for physicists. We summarize in this note some of their basic homotopy theoretic properties and derive a handful of known…
In this paper we consider the isoptic curves on the 2-dimensional geometries of constant curvature $\bE^2,~\bH^2,~\cE^2$. The topic is widely investigated in the Euclidean plane $\bE^2$ see for example \cite{CMM91} and \cite{Wi} and the…
We study the generalized analogues of conics for normed planes by using the following natural approach: It is well known that there are different metrical definitions of conics in the Euclidean plane. We investigate how these definitions…
We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…
In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.
In this paper, we establish a second main theorem for holomorphic curve intersecting hypersurfaces in general position in projective space with level of truncation. As an application, we reduce the number hypersurfaces in uniqueness problem…
In this work, we solve the problem of finding non-intersecting paths between points on a plane with a new approach by borrowing ideas from geometric topology, in particular, from the study of polygonal schema in mathematics. We use a…
A basic problem in computer vision is to understand the structure of a real-world scene given several images of it. Here we study several theoretical aspects of the intra multi-view geometry of calibrated cameras when all that they can…