共查询到20条相似文献,搜索用时 15 毫秒
1.
《Indagationes Mathematicae》2014,25(5):977-991
We introduce the notion of matched pairs of Courant algebroids and give several examples arising naturally from complex manifolds, holomorphic Courant algebroids, and certain regular Courant algebroids. We also consider the matched sum of two Dirac subbundles, one in each of two Courant algebroids forming a matched pair. 相似文献
2.
3.
Yunhe Sheng 《代数通讯》2013,41(5):1929-1953
Let Y be an integral projective curve whose singularities are of type Ak, i.e. with only tacnodes and planar (perhaps non-ordinary) cusps. Set g:= pa(Y). Here we study the Brill - Noether theory of spanned line bundles on Y. If the singularities are bad enough, we show the existence of spanned degree d line bundles, L, with h0(Y, L) ≥ r + 1 even if the Brill - Noether number ρ(g, d, r) < 0. We apply this result to prove that genus g curves with certain singularities cannot be hyperplane section of a simple K3 surface S ? P g. 相似文献
4.
BI YanHui & SHENG YunHe 《中国科学 数学(英文版)》2011,(3):437-447
In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle TM ⊕∧nT*M for an m-dimensional manifold. As an application, we revisit Nambu-Poisson structures and multisymplectic structures. We prove that the graph of an (n + 1)-vector field π is closed under the higher-order Dorfman bracket iff π is a Nambu-Poisson structure. Consequently, there is an induced Leibniz algebroid structure on ∧nT*M. The graph of an (n+1)-form ω is closed under... 相似文献
5.
This note studies invariant generators for a certain class of invariant smooth generalized subbundles of exact Courant algebroids, which generalizes existing results for invariant vector subbundles of exact Courant algebroids. As a result, we provide a simple and geometric proof for Theorem 1 in [1]. 相似文献
6.
Brett Milburn 《Differential Geometry and its Applications》2011,29(5):615-641
The aim of this paper is to study generalized complex geometry (Hitchin, 2002) [6] and Dirac geometry (Courant, 1990) [3], (Courant and Weinstein, 1988) [4] on homogeneous spaces. We offer a characterization of equivariant Dirac structures on homogeneous spaces, which is then used to construct new examples of generalized complex structures. We consider Riemannian symmetric spaces, quotients of compact groups by closed connected subgroups of maximal rank, and nilpotent orbits in sln(R). For each of these cases, we completely classify equivariant Dirac structures. Additionally, we consider equivariant Dirac structures on semisimple orbits in a semisimple Lie algebra. Here equivariant Dirac structures can be described in terms of root systems or by certain data involving parabolic subalgebras. 相似文献
7.
8.
9.
A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of equivalence. In this setting, we are able to construct characteristic classes, which in special cases reproduce characteristic classes constructed by Crainic and Fernandes. We give a complete classification of regular VB-algebroids, and in the process we obtain another characteristic class of Lie algebroids that does not appear in the ordinary representation theory of Lie algebroids. 相似文献
10.
Anthony D. Blaom 《Transactions of the American Mathematical Society》2006,358(8):3651-3671
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 algebroid structure. The curvature of this connection vanishes precisely when the structure is locally symmetric.
This model generalizes Cartan geometries, a substantial class, to the intransitive case. Simple examples are surveyed and corresponding local obstructions to symmetry are identified. These examples include foliations, Riemannian structures, infinitesimal -structures, symplectic and Poisson structures.
11.
We introduce the notion of Atiyah class of a generalized holomorphic vector bundle, which captures the obstruction to the existence of generalized holomorphic connections on the bundle. As in the classical holomorphic case, this Atiyah class can be defined in three different ways: using Čech cohomology, using the first-jet short exact sequence, or adopting the Lie pair point of view. 相似文献
12.
首先陈述Leibniz代数胚上的动力系统和在局部坐标系下该动力系统的方程,在此基础上,给出了动力系统轨道的范例和图示. 相似文献
13.
14.
15.
Michael Kunzinger 《Journal of Mathematical Analysis and Applications》2004,297(2):456-471
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in nonsmooth differential geometry. This article presents an introductory survey of recent developments in this field and highlights some applications in mathematical physics. 相似文献
16.
Hongzhu Gao 《中国科学A辑(英文版)》1989,42(6):586-592
Let σ be an anti-holomorphic involution on almost complex manifoldX, the existence of almost complex structure onY=X/σ is discussed.
Project supported by the National Natural Science Foundation of China (Grant No. 19771010). 相似文献
17.
Donglong Li Zhengde Dai Xuhong Liu 《Journal of Mathematical Analysis and Applications》2007,330(2):934-948
In this paper, the two-dimensional generalized complex Ginzburg–Landau equation (CGL)
ut=ρu−Δφ(u)−(1+iγ)Δu−νΔ2u−(1+iμ)|u|2σu+αλ1(|u|2u)+β(λ2)|u|2