共查询到16条相似文献,搜索用时 125 毫秒
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本文首先建立球面型空间中度量平均的概念,其次讨论度量平均过程中一些几何不变量之间的关系,最后举例说明度量平均在解决球面型空间中几何极值问题时的应用. 相似文献
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本文研究了上半空间和单位球上的调和Bergman-Orlicz空间的刻画及调和函数差商的有界性.给出了调和Bergman-Orlicz空间分别在欧氏度量,双曲型度量,伪双曲型度量下的Lipschitz型刻画.利用这些刻画获得了调和函数差商的有界性,这些结果推广了相应于上半空间和单位球上的调和Bergman空间上的结果. 相似文献
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本文改进了杨世国关于非欧空间中基本图形的度量方程,建立一个一般意义下的、应用更为方便的广义度量方程,作为其初步应用,导出了非欧空间中两个单形之间的一些有趣的几何关系. 相似文献
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本文研究了Bloch型空间中函数性质问题.利用拟双曲度量及一些不等式得到了Bloch型空间B~α(B_n)(0α≤1)的一个新的刻画,该刻画将Bloch型空间B~α(B_n)的Holland-Walsh刻画推广到一个高阶形式. 相似文献
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本文主要考虑度量空间中拟双曲一致域与拟对称映射之间的关系,并证明了度量空间中拟双曲一致域在拟对称映射下仍然是保持不变的. 相似文献
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本文提出并解决了初等图形在球面型空间实现的问题: 预给两两之间度量的几何元素e1,e2…,el-1,el+1,…,eN(ei为点或超平面),初等图形{e1,…,el-1,el+1,…,eN}在球面型空间实现的充分必要条件是什么? 相似文献
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Spherical spline quaternion interpolation has been done on sphere in Euclidean space using quaternions. In this paper, we have done the spline split quaternion interpolation on hyperbolic sphere in Minkowski space using split quaternions and metric Lorentz. This interpolation curve is called spherical spline split quaternion interpolation in Minkowski space (MSquad). 相似文献
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Projectively equivalent metrics, exact transverse line fields and the geodesic flow on the ellipsoid
S. Tabachnikov 《Commentarii Mathematici Helvetici》1999,74(2):306-321
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This paper considers the question of relative hyperbolicity of an Artin group with regard to the geometry of its associated
Deligne complex. We prove that an Artin group is weakly hyperbolic relative to its finite (or spherical) type parabolic subgroups
if and only if its Deligne complex is a Gromov hyperbolic space. For a two-dimensional Artin group the Deligne complex is
Gromov hyperbolic precisely when the corresponding Davis complex is Gromov hyperbolic, that is, precisely when the underlying
Coxeter group is a hyperbolic group. For Artin groups of FC type we give a sufficient condition for hyperbolicity of the Deligne
complex which applies to a large class of these groups for which the underlying Coxeter group is hyperbolic. The key tool
in the proof is an extension of the Milnor-Svarc Lemma which states that if a group G admits a discontinuous, co-compact action by isometries on a Gromov hyperbolic metric space, then G is weakly hyperbolic relative to the isotropy subgroups of the action.
相似文献
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Immanuel Asmus 《Journal of Geometry》2009,96(1-2):11-40
We study the trigonometry on the de Sitter surface. Since this surface carries a metric of Lorentzian signature, care has to be taken when defining lengths and angles. We provide trigonometric formulae for triangles of all causality types. This is basically achieved by transferring the concept of polar triangles from spherical geometry into the Minkowski space. As a byproduct, we obtain a new simple proof of the hyperbolic law of cosines for angles. 相似文献
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J.-M. Schlenker 《Geometric And Functional Analysis》2002,12(2):395-435
A classical theorem, mainly due to Aleksandrov [Al2] and Pogorelov [P], states that any Riemannian metric on S
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with curvature K > —1 is induced on a unique convex surface in H
3
. A similar result holds with the induced metric replaced by the third fundamental form. We show that the same phenomenon
happens with yet another metric on immersed surfaces, which we call the horospherical metric.?This result extends in higher
dimensions, the metrics obtained are then conformally flat. One can also study equivariant immersions of surfaces or the metrics
obtained on the boundaries of hyperbolic 3-manifolds. Some statements which are difficult or only conjectured for the induced
metric or the third fundamental form become fairly easy when one considers the horospherical metric, which thus provides a
good boundary condition for the construction of hyperbolic metrics on a manifold with boundary.?The results concerning the
third fundamental form are obtained using a duality between H
3
and the de Sitter space . In the same way, the results concerning the horospherical metric are proved through a duality between H
n
and the space of its horospheres, which is naturally endowed with a fairly rich geometrical structure.
Submitted: March 2001, Revised: November 2001. 相似文献
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THE FOUR-DIMENSIONAL HYPERBOLIC SPHERICAL HARMONICS 总被引:14,自引:0,他引:14
In the four-dimensional hyperbolic space, we can derive Euler formula and establish the hyperbolic spherical polar coordinate
and the hyperbolic spherical harmonics. 相似文献