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1.
Kobayashi's and Teichm¨uller's Metrics and Bers Complex Manifold Structure on Circle Diffeomorphisms
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《数学学报(英文版)》2020,(3)
Given a modulus of continuity ω,we consider the Teichmuller space TC~(1+ω) as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit disk.We study several distortion properties for diffeomorphisms and quasisymmetric homeomorphisms.Using these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC~(1+H) as the union of over all0 α≤1,which turns out to be the largest space in the Teichmuller space of C~1 orientation-preserving circle diffeomorphisms on which we can assign such a structure.Furthermore,we prove that with the Bers complex manifold structure on TC~(1+H),Kobayashi's metric and Teichmuller's metric coincide. 相似文献
2.
CAI Yongmao & SHEN Yuliang Department of Mathematics Suzhou University Suzhou China 《中国科学A辑(英文版)》2006,(5)
It is proved that for any Fuchsian group Г such that H/Г is a hyperbolic Riemann surface, the Teichmuller curve V(Г) has a unique complex manifold structure so that the natural projection of the Bers fiber space F(Г) onto V(Г) is holomorphic with local holomorphic sections. An isomorphism theorem for Teichmuller curves is deduced, which generalizes a classical result that the Teichmuller curve V(Г) depends only on the type of Г and not on the orders of the elliptic elements of Г when H/Г is a compact hyperbolic Riemann surface. 相似文献
3.
The present paper is devoted to determining the metric g for an n-dimension-al (n≥4) Riemannian manifold (M, g) of quasi-constant curvature [1]. By the way, we have identified the space of quasi-constant curvature with the κ-special conformally flat space of K.Yano & B.Y.Chen [8]. Based upon the results so obtained, we have completely determined the canonical metric for such a space to admit the relevant field X as geodesic field, and the geometric structure for (M, g) to be a recurrent space of quasi-constant curvature. Also we have examined the validity of our results just obtained for a 3-dimensional conformally flat space of quasi-constant cvrvature. Besides, we have deduced some global properties of a complete manifold of quasi-constant curvature, which may be useful in applications. 相似文献
4.
The present paper is devoted to determining the metric g for an n-dimensional (n≥4) Riemannian manifold (M, g) of quasi-constant curvature [1]. By the way, we have identified the space of quasi-constant curvature with the k-special conformally flat space of K. Yano & B. Y. Chen [8]. Based upon the results so obtained, we have completely determined the canonical metric for such a space to admit the relevant field X as geodesic field, and the geometric structure for (M, g) to be a recurrent space of quasi-constant curvature. Also we have examined the validity of our results just obtained for a 3-dimensional conformally flat space of quasi-constant cvrvature. Besides, we have deduced some global properties for a complete manifold of quasi-constant curvature, which may be useful in applications. 相似文献
5.
Given a real (finite-dimensional or infinite-dimensional) Hilbert space H with a Jordan product, we introduce the concepts of ω-unique and ω-P properties for linear transformations on H, and investigate some interconnections among these concepts. In particular, we discuss the ω-unique and ω-P properties for Lyapunov-like transformations on H. The properties of the Jordan product and the Lorentz cone in the Hilbert space play important roles in our analysis. 相似文献
6.
《中国科学 数学(英文版)》2016,(2)
An n × n ω-circulant matrix which has a specific structure is a type of important matrix. Several norm equalities and inequalities are proved for ω-circulant operator matrices with ω = e~(iθ)(0≤θ 2π) in this paper. We give the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norms. Pinching type inequality is also proposed for weakly unitarily invariant norms. Meanwhile,we present that the set of ω-circulant matrices with complex entries has an idempotent basis. Based on this basis, we introduce an automorphism on the ω-circulant algebra and then show different operators on linear vector space that are isomorphic to the ω-circulant algebra. The function properties, other idempotent bases and a linear involution are discussed for ω-circulant algebra. These results are closely related to the special structure of ω-circulant matrices. 相似文献
7.
Geometric aspects of the moduli space of Riemann surfaces 总被引:10,自引:0,他引:10
Shing-Tung Yau 《中国科学A辑(英文版)》2005,48(Z1)
We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kahler metrics were introduced on the moduli space and Teichmuller space. Their curvature properties and asymptotic behavior were studied in details. These natural metrics served as bridges to connect all the known canonical metrics, especially the Kahler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincare type growth. Furthermore, the Kahler-Einstein metric has strongly bounded geometry. This also implied that the logarithm cotangent bundle of the moduli space is stable in the sense of Mumford. 相似文献
8.
Lian Fa HE College of Mathematics Information Science Hebei Normal University Shijiazhuang P.R.ChinaJin Feng LV Hebei Normal University of Science & Technology Qinhuangdao P.R.China Li Na ZHOU College of Mathematics Information Science Hebei Normal University Shijiazhuang P.R.China 《应用数学学报(英文版)》2004,(4)
We introduce a new definition of measure-theoretic pressure for ergodic measures of con-tinuous maps on a compact metric space.This definition is similar to those of topological pressureinvolving spanning sets.As an application,for C~(1 α)(α>0) diffeomorphisms of a compact manifold,we study the relationship between the measure-theoretic pressure and the periodic points. 相似文献
9.
A non-Euclidean crystallographic group F (NEC group, for short) is a discrete subgroup of isometries of the hyperbolic plane H, with compact quotient space H/Г. These groups uniformize Klein surfaces, surfaces endowed with dianalytic structure. These surfaces can be seen as a generalization of Riemann surfaces.
Fundamental polygons play an important role in the study of parametrizations of the Teichmuller space of NEC groups.
In this work we construct a class of right-angled polygons which are fundamental regions of bordered surface NEC groups. The free parameters used in the construction of the polygons give a parametrization of the Teichmuller space. From the parameters we obtain explicit matrices of the generators of the groups. Finally, we give examples to exhibit how different relations between the parameters reflect the existence of automorphisms on the quotient surfaces. 相似文献
Fundamental polygons play an important role in the study of parametrizations of the Teichmuller space of NEC groups.
In this work we construct a class of right-angled polygons which are fundamental regions of bordered surface NEC groups. The free parameters used in the construction of the polygons give a parametrization of the Teichmuller space. From the parameters we obtain explicit matrices of the generators of the groups. Finally, we give examples to exhibit how different relations between the parameters reflect the existence of automorphisms on the quotient surfaces. 相似文献
10.
Under the assumption that' is a strongly convex weakly Khler Finsler metric on a complex manifold M, we prove that F is a weakly complex Berwald metric if and only if F is a real Landsberg metric.This result together with Zhong(2011) implies that among the strongly convex weakly Kahler Finsler metrics there does not exist unicorn metric in the sense of Bao(2007). We also give an explicit example of strongly convex Kahler Finsler metric which is simultaneously a complex Berwald metric, a complex Landsberg metric,a real Berwald metric, and a real Landsberg metric. 相似文献
11.
Abdlkadir ZDEGER 《数学学报(英文版)》2013,29(2):373-382
It is well known that the Einstein tensor G for a Riemannian manifold defined by G βα = R βα 1/2 Rδβα , R βα = g βγ R γα where R γα and R are respectively the Ricci tensor and the scalar curvature of the manifold, plays an important part in Einstein's theory of gravitation as well as in proving some theorems in Riemannian geometry. In this work, we first obtain the generalized Einstein tensor for a Weyl manifold. Then, after studying some properties of generalized Einstein tensor, we prove that the conformal invariance of the generalized Einstein tensor implies the conformal invariance of the curvature tensor of the Weyl manifold and conversely. Moreover, we show that such Weyl manifolds admit a one-parameter family of hypersurfaces the orthogonal trajectories of which are geodesics. Finally, a necessary and sufficient condition in order that the generalized circles of a Weyl manifold be preserved by a conformal mapping is stated in terms of generalized Einstein tensors at corresponding points. 相似文献
12.
Let Г be a Fuchsian group acting on the upper half plane H. We denote byBel(Г) the set of all Beltrami differentials of Г on H with L~∞-norms less than 1.For each μ∈Bel(Г) there exists a uniquely determiued quasiconformal mapping f_μ:H→H with the complex dilatation μ, which keeps 0,1 and ∞ fixed. Two elementsμ_1 and μ_2 of Bel(Г) are said to be equivalent each other if f_(μ1)|R coincides withf_(μ2) |R. Then the Teichmuller space of Г is defined to be the set of all equivalenceclasses of elements in Bel(Г). 相似文献
13.
Ngaiming Mok 《中国科学A辑(英文版)》2005,(Z1)
We study holomorphic immersions f:X→M from a complex manifold X into a Kahler manifold of constant holomorphic sectional curvature M, i.e. a complex hyperbolic space form, a complex Euclidean space form, or the complex projective space equipped with the Fubini-Study metric. For X compact we show that the tangent sequence splits holomorphically if and only if f is a totally geodesic immersion. For X not necessarily compact we relate an intrinsic cohomological invariant p(X) on X, viz. the invariant defined by Gunning measuring the obstruction to the existence of holomorphic projective connections, to an extrinsic cohomological invariant v(f) measuring the obstruction to the holomorphic splitting of the tangent sequence. The two invariants p(X) and v(f) are related by a linear map on cohomology groups induced by the second fundamental form. In some cases, especially when X is a complex surface and M is of complex dimension 4, under the assumption that X admits a holomorphic projective connection we obtain 相似文献
14.
SUN Xiaowei WANG Youde 《偏微分方程(英文版)》2010,(2):203-208
We define a kind of KdV (Korteweg-de Vries) geometric flow for maps from a real line or a circle into a Kahler manifold (N,J,h) with complex structure J and metric h as the generalization of the vortex filament dynamics from a real line or a circle. By using the geometric analysis, the existence of the Cauchy problems of the KdV geometric flows will be investigated in this note. 相似文献
15.
Zhenqian Li 《中国科学 数学(英文版)》2024,(5):951-974
In this article, we introduce multiplier ideal sheaves on complex spaces with singularities(not necessarily normal) via Ohsawa’s extension measure, as a special case of which, it turns out to be the socalled Mather-Jacobian multiplier ideals in the algebro-geometric setting. Inspired by Nadel’s coherence and Guan-Zhou’s strong openness properties of the multiplier ideal sheaves, we discuss similar properties for the generalized multiplier ideal sheaves. As applications, we obtain a reasonable ge... 相似文献
16.
Chong Wu 《中国科学 数学(英文版)》2012,55(3):625-632
Let QS* (S 1) be the space of quasisymmetric homeomorphisms of the unit circle such that the corresponding subspace of the universal Teichmu¨ller space has Weil-Petersson metric.In this paper we give a necessary condition for a quasisymmetric homeomorphism to belong to QS *(S 1) from the aspect of cross-ratio distortion. 相似文献
17.
MATHAI Varghese 《中国科学 数学(英文版)》2010,(3)
We review the Reidemeister, Ray-Singer’s analytic torsion and the Cheeger-Mller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties. We define a new twisted analytic torsion for the complex of invariant differential forms on the total space of a principal circle bundle twisted by an invariant flux form. We show that when the dimension is even, such a torsion is invariant under certain deformation of the metric and the flux form. Under T-duality which exchanges the topology of the bundle and the flux form and the radius of the circular fiber with its inverse, the twisted torsion of invariant forms are inverse to each other for any dimension. 相似文献
18.
LIAO Gongfu WANG Lidong & ZHANG Yucheng Institute of Mathematics Jilin University Changchun China Institute of Nonlinear Information Technology Dalian Nations University Dalian China Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2006,49(1):1-8
Consider the continuous map f : x → X and the continuous map f of K,(X) into itself induced by f, where X is a metric space and K(X) the space of all non-empty compact subsets of x endowed with the Hausdorff metric. According to the questions whether the chaoticity of f implies the chaoticity of f posed by Roman-Flores and when the chaoticity of f implies the chaoticity of f posed by Fedeli, we investigate the relations between f and f in the related dynamical properties such as transitivity, weakly mixing and mixing, etc. And by using the obtained results, we give the satisfied answers to Roman-Flores's question and Fedeli's question. 相似文献
19.
Pei-xin YeInstitute of Mathematics Academy of Mathematics System Sciences Chinese Academy of Science Beijing 《应用数学学报(英文版)》2002,(3)
The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space. 相似文献
20.
We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T0(M)). T0(M) denotes the Teichm¨uller space of all negatively curved Riemannian metrics on M, which is the topological quotient of the space of all negatively curved metrics modulo the space of self-diffeomorphisms of M that are homotopic to the identity. 相似文献