共查询到20条相似文献,搜索用时 93 毫秒
1.
狭义相对论的变革点就是相对时空观,而相对论时空与非欧几何学有着密切的联系.在介绍了传统的Minkowski空间后,引入双曲虚单位,其所构造的双曲复数对应双曲Minkowski复空间.利用双曲Minkowski空间复数运算规则,可以使高速运动客体的物理规律与复数的性质结合起来,为解决狭义相对论的普遍形式提供新的数学工具. 相似文献
2.
NoělLohoué证明了复对称空间上某种极大函数f+(x)=supt>0(1+t)32|Ptf(x)|的可和性可归结为‖(Δ0)12f‖(x)的可和性.作者证明了上述结果对奇数维实双曲空间成立.由于偶数维实双曲空间的热核表达式不同,因此有必要对偶数维实双曲空间的情形单独给出证明.本文的目的就是证明上述结果对偶数维实双曲空间亦成立. 相似文献
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将多元复分析中一种复偏微分方程组的解与复Clifford分析中双曲调和函数联系起来,并研究了双曲调和函数的几个性质。 相似文献
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本文的主要定理是:对每一个正数V,存在一个D>0,如果一个3维黎曼流形M的体积小于V,截面曲率在-1和0之间,而且直径大于D,那么M允许一个双曲结构。 相似文献
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设M是2维复双曲空间CH^2中的具有三个不同常数主曲率的实超曲面,则M满足下列之一:(1)其中有两个主曲率之间的差界于0和1之间;(2)三个主曲率形成一个公差是1的等差数列;(3)M全纯重合于二维实双曲空间上的一个管子。 相似文献
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<正> §2.1.引言Lie 球双曲空间■(以下记为■),由满足■的 N(≥2)个复元素矢量 z=(z_1,z_2,…,z_N)所构成.■的边界,记为■,特別地,以(■表示■的特征流形.此外,N(≥2)个复变数 z_1,…,z_N 空间中的域■, 相似文献
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<正> 3.1.斜对称方阵双曲空间的调和函数 命 Z 代表 n×n 斜对称方阵(?)(?)个复变数 z_(12),z_(13),…z_(1n),z_(23),…,(?)…,z_(n-1,n)空间的域我们引进运算子 相似文献
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<正> §3.1.引言(m,n)表示矩阵双曲空间:(?)表示空间:(?)Z 是 m 行 n 列(不妨设 m≤n)复元素矩阵.华罗庚指出:如果甲(?)(U)在(m,n)的特征流形(?)上连续,则(?)的 Cauchy 型积分 相似文献
11.
Yu Xuegang 《Advances in Applied Clifford Algebras》2000,10(1):49-60
The hyperbolic complex space is one class of non-Euclidean spaces with continuous singular points. It corresponds with Minkowski
space, and it has the characteristic that the space-time direction is different in nature. Regard the hyperbolic complex space
as original spaces. We can abstract a class of the hyperbolic inner product space and the hyperbolic Hilbert space. 相似文献
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Haotian Wu 《Geometriae Dedicata》2013,164(1):231-258
Using the maximal regularity theory for quasilinear parabolic systems, we prove two stability results of complex hyperbolic space under the curvature-normalized Ricci flow in complex dimensions two and higher. The first result is on a closed manifold. The second result is on a complete noncompact manifold. To prove both results, we fully analyze the structure of the Lichnerowicz Laplacian on complex hyperbolic space. To prove the second result, we also define suitably weighted little Hölder spaces on a complete noncompact manifold and establish their interpolation properties. 相似文献
15.
Adel Khalfallah 《Mathematische Zeitschrift》2007,255(4):691-702
In this paper, we construct the moduli space of reduced hyperbolic compact complex spaces. First, we prove an infinitesimal
characterization of hyperbolicity using a family of Kobayashi–Royden pseudo-metrics introduced by Venturini and as a consequence
we conclude that the property of Landau holds for complex spaces. Finally, we establish this moduli space in the case of locally
trivial deformations, and in a more general situation, the case of equisingular deformations. 相似文献
16.
W. A. Kirk 《Numerical Functional Analysis & Optimization》2013,34(4):371-381
A well-known iteration scheme due to Krasnoselskii for approximation of fixed points of nonexpansive mappings in Banach spaces is extended to a wider class of spaces. This class includes convex metric spaces of ‘hyperbolic’ type, and the results apply to the study of holomorphic self-mappings of the unit ball in complex Hilbert space. 相似文献
17.
Duc-Manh Nguyen 《Geometric And Functional Analysis》2010,20(1):192-228
In this paper, we study the moduli spaces of flat surfaces with cone singularities verifying the following property: there
exists a union of disjoint geodesic tree on the surface such that the complement is a translation surface. Those spaces can
be viewed as deformations of the moduli spaces of translation surfaces in the space of flat surfaces. We prove that such spaces
are quotients of flat complex affine manifolds by a group acting properly discontinuously, and preserving a parallel volume
form. Translation surfaces can be considered as a special case of flat surfaces with erasing forest, in this case, it turns
out that our volume form coincides with the usual volume form (which are defined via the period mapping) up to a multiplicative
constant. We also prove similar results for the moduli space of flat metric structures on the n-punctured sphere with prescribed
cone angles up to homothety. When all the angles are smaller than 2π, it is known (cf. [T]) that this moduli space is a complex hyperbolic orbifold. In this particular case, we prove that our
volume form induces a volume form which is equal to the complex hyperbolic volume form up to a multiplicative constant. 相似文献
18.
It is shown that, by applying hyperbolic isometries, one may arrangen points in hyperbolic (n–1)-space in a certain standard position. Similar results are developed for complex hyperbolic space, as well as hyperbolic spaces defined over nearly arbitrary fields. The algebraic basis of the paper is the determination of the structure of a double coset space which occurs in representation theory.Partially supported by NSA grant # MDA-904-96-0018.Partially supported by NSA grant # MDA904-95-1-1089. 相似文献
19.
Alfonso Romero 《manuscripta mathematica》1987,59(3):261-276
The rigidity for full holomorphic isometric immersions of an indefinite Kähler manifold into an indefinite complex space form is proved. All such immersions between indefinite complex projective (and hyperbolic) spaces are founded and examples of non-congruents holomorphic isometric immersions are exposed. 相似文献
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Georgios Daskalopoulos Chikako Mese Alina Vdovina 《Geometric And Functional Analysis》2011,21(4):905-919
In this paper, we study the behavior of harmonic maps into complexes with branching differentiable manifold structure. The
main examples of such target spaces are Euclidean and hyperbolic buildings. We show that a harmonic map from an irreducible
symmetric space of noncompact type other than real or complex hyperbolic into these complexes are non-branching. As an application,
we prove rank-one and higher-rank superrigidity for the isometry groups of a class of complexes which includes hyperbolic
buildings as a special case. 相似文献