共查询到20条相似文献,搜索用时 203 毫秒
1.
本文借助于Riemann曲面上的长度谱与极大环域的模,给出了任意的Riemann曲面间存在拟共形同胚的必要条件,并给出了一类特殊无限型Riemann曲面间有拟共形同胚的充要条件.尤其是,证明了一类Teichmuller映射的极值性,将紧致曲面上的Teichmuller的一个定理推广到任意的Riemann曲面上. 相似文献
2.
3.
4.
在本文中,我们处理在任意开Riemann曲面F上一类解析微分的A周期问题. 1.记号 我们沿用Ahlfors[2]中的记号.T和T~1表示Riemann曲面F上所有平方可和的可测系数的或连续可微系数的微分所成的空间.我们还用到下面的子空间: 相似文献
5.
本文在紧Riemann曲面上引入了拟距离函数和圆环域的概念,并给出了这种圆环域上的Hadamard定理. 相似文献
6.
Riemann曲面M上的平方可测1-形式全体和解析1-形式全体均可构成Hilbert空间.本文讨论Riemann曲面上的解析映射导出的这类Hilbert空间上的复合算子,研究复合算子的正常性、拟正常性的诱导映射特征.特别地,当M有有限三角剖分时,证明了正常复合算子、拟正常复合算子、酉复合算子、等距复合算子和可逆复合算子等价. 相似文献
7.
本文主要考虑循环群作用 Riemann曲面的分类问题 ,我们列出了所有的循环群作用亏格为 4Riem ann曲面的拓扑分类和弱拓扑分类 相似文献
8.
该文从1+1维的孤子方程出发,构造出一个2+1维在Lax意义下可积的方程.接着这个2+1维可积方程被分解为可解的常微分方程.随后引入超椭圆Riemann曲面和Abel-Jacobi坐标把流进行了拉直.再利用Riemannθ函数给出了这个2+1维方程的代数几何解. 相似文献
9.
10.
一族曲面切族芽是一系列正则曲面的运动,这种运动是从一个正则曲面切变到另一个正则曲面.文中给出了在形变意义下稳定的曲面切族芽的分类,并且研究了它们的包络的奇点. 相似文献
11.
Envelopes of splines in the projective plane 总被引:2,自引:0,他引:2
In this paper a family of curvesRiemannian cubicsinthe unit sphere and the real projective plane is investigated.Riemannian cubics naturally arise as solutions to variationalproblems in Riemannian spaces. It is remarkable to find thatan envelope of lines generated by a Riemannian cubic in onespace is (nearly) a Riemannian cubic in another space. 相似文献
12.
We show that certain right-invariant metrics endow the
infinite-dimensional Lie group of all smooth
orientation-preserving diffeomorphisms of the circle with a
Riemannian structure. The study of the Riemannian exponential map
allows us to prove infinite-dimensional counterparts of results
from classical Riemannian geometry: the Riemannian exponential map is
a smooth local diffeomorphism and the length-minimizing property of
the geodesics holds. 相似文献
13.
Sebastian Klein 《Geometriae Dedicata》2009,138(1):25-50
The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature
tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from
its Satake diagram, in a way that is suited for the use with computer algebra systems; an example implementation for Maple Version 10 can be found on . As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified.
相似文献
14.
H. Ghahremani-Gol A. Razavi 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2016,51(5):215-221
The Ricci flow is an evolution equation in the space of Riemannian metrics.A solution for this equation is a curve on the manifold of Riemannian metrics. In this paper we introduce a metric on the manifold of Riemannian metrics such that the Ricci flow becomes a geodesic.We show that the Ricci solitons introduce a special slice on the manifold of Riemannian metrics. 相似文献
15.
Marija S. ?iri? Milan Lj. Zlatanovi? Mi?a S. Stankovi? Ljubica S. Velimirovi? 《Applied mathematics and computation》2012,218(12):6648-6655
In this paper geodesic mappings of equidistant generalized Riemannian spaces are discussed. It is proved that each equidistant generalized Riemannian space of basic type admits non-trivial geodesic mapping with preserved equidistant congruence. Especially, there exists non-trivial geodesic mapping of equidistant generalized Riemannian space onto equidistant Riemannian space. An example of geodesic mapping of an equidistant generalized Riemannian spaces is presented. 相似文献
16.
Brian Clarke 《Calculus of Variations and Partial Differential Equations》2010,39(3-4):533-545
We prove that the L 2 Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold induces a metric space structure. As the L 2 metric is a weak Riemannian metric, this fact does not follow from general results. In addition, we prove several results on the exponential mapping and distance function of a weak Riemannian metric on a Hilbert/Fréchet manifold. The statements are analogous to, but weaker than, what is known in the case of a Riemannian metric on a finite-dimensional manifold or a strong Riemannian metric on a Hilbert manifold. 相似文献
17.
Lyle Noakes 《Advances in Computational Mathematics》2002,17(4):385-395
Riemannian quadratics are C
1 curves on Riemannian manifolds, obtained by performing the quadratic recursive deCastlejeau algorithm in a Riemannian setting. They are of interest for interpolation problems in Riemannian manifolds, such as trajectory-planning for rigid body motion. Some interpolation properties of Riemannian quadratics are analysed when the ambient manifold is a sphere or projective space, with the usual Riemannian metrics. 相似文献
18.
A Riemannian orbifold is a mildly singular generalization of a Riemannian manifold which is locally modeled on the quotient of a connected, open manifold under a finite group of isometries. If all of the isometries used to define the local structures of an entire orbifold are orientation preserving, we call the orbifold locally orientable. We use heat invariants to show that a Riemannian orbifold which is locally orientable cannot be Laplace isospectral to a Riemannian orbifold which is not locally orientable. As a corollary we observe that a Riemannian orbifold that is not locally orientable cannot be Laplace isospectral to a Riemannian manifold. 相似文献
19.
Bayram Sahin 《Proceedings Mathematical Sciences》2008,118(4):573-581
We study harmonic Riemannian maps on locally conformal Kaehler manifolds (lcK manifolds). We show that if a Riemannian holomorphic
map between lcK manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map
under a condition. When the domain is Kaehler, we prove that a Riemannian holomorphic map is harmonic if and only if the lcK
manifold is Kaehler. Then we find similar results for Riemannian maps between lcK manifolds and Sasakian manifolds. Finally,
we check the constancy of some maps between almost complex (or almost contact) manifolds and almost product manifolds. 相似文献
20.
The article presents an information about the Laplace operator defined on the real-valued mappings of compact Riemannian manifolds,
and its spectrum; some properties of the latter are studied. The relationship between the spectra of two Riemannian manifolds
connected by a Riemannian submersion with totally geodesic fibers is established. We specify a method of calculating the spectrum
of the Laplacian for simply connected simple compact Lie groups with biinvariant Riemannian metrics, by representations of
their Lie algebras. As an illustration, the spectrum of the Laplacian on the group SU(2) is found. 相似文献