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31.
32.
Jerzy Kocik 《Advances in Applied Clifford Algebras》2007,17(1):71-93
We show that the space of Euclid’s parameters for Pythagorean triples is endowed with a natural symplectic structure and that
it emerges as a spinor space of the Clifford algebra R21, whose minimal version may be conceptualized as a 4-dimensional real algebra of “kwaternions.” We observe that this makes
Euclid’s parametrization the earliest appearance of the concept of spinors. We present an analogue of the “magic correspondence”
for the spinor representation of Minkowski space and show how the Hall matrices fit into the scheme. The latter obtain an
interesting and perhaps unexpected geometric meaning as certain symmetries of an Apollonian gasket. An extension to more variables
is proposed and explicit formulae for generating all Pythagorean quadruples, hexads, and decuples are provided. 相似文献
33.
Wu Yang YU Dong Hua WU Gang Song LENG 《数学学报(英文版)》2007,23(11):1937-1948
The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the quasi Lp-intersection bodies are obtained. The Aleksandrov Fenchel inequality for the mixed quasi Lp-intersection bodies is also established. 相似文献
34.
关于射影平坦Finsler空间 总被引:4,自引:0,他引:4
本文研究了射影平坦Finsler空间的几何量及其几何性质。证明了射影平坦Finsler空间的Ricci曲率可完全由射影因子简洁地刻画出来。同时还证明了,在射影平坦Finsler空间中,平均Berwald曲率S=0意味着Ricci曲率Ric是二次齐次的。此外,给出了一个射影平坦Finsler空间成为常曲率空间或局部Minkowski空间的充分条件。 相似文献
35.
Summary The purpose of this paper is to establish extremal values for inner and
outer radii of the unit ball of a Minkowski space for the Holmes--Thompson and
Busemann measures. Furthermore, we confirm a conjecture of C. A. Rogers and G. C. Shephard on ellipsoids. 相似文献
36.
本文在[1]的基础上继续研究了三维Minkowski空间E31中,直线汇异于欧式空间的一些性质. 相似文献
37.
In this paper, we study the relations between a compact spacelike hypersurface with hy-perplanar boundary in the (n 1)- dimensional Minkowski space-time L^n 1 being totally umbilicaland its hyperplanar boundary in a fixed hyperplane π of L^(n 1) being totally umbilical under certainconditions. We give the sufficient conditions for such hypersurface and its hyperplanar boundary tobe totally umbilical in their respective ambients. 相似文献
39.
Hans Raj Tiwary 《Discrete and Computational Geometry》2008,40(3):469-479
For polytopes P
1,P
2⊂ℝ
d
, we consider the intersection P
1∩P
2, the convex hull of the union CH(P
1∪P
2), and the Minkowski sum P
1+P
2. For the Minkowski sum, we prove that enumerating the facets of P
1+P
2 is NP-hard if P
1 and P
2 are specified by facets, or if P
1 is specified by vertices and P
2 is a polyhedral cone specified by facets. For the intersection, we prove that computing the facets or the vertices of the
intersection of two polytopes is NP-hard if one of them is given by vertices and the other by facets. Also, computing the
vertices of the intersection of two polytopes given by vertices is shown to be NP-hard. Analogous results for computing the
convex hull of the union of two polytopes follow from polar duality. All of the hardness results are established by showing
that the appropriate decision version, for each of these problems, is NP-complete. 相似文献
40.
RemarksontheVeroneseGeneratingSubmanifoldsinMinkoskiSpaceHuConge(胡聪娥)(HenanUniversity,Kaifeng,475001)Abstract:Inthispaper,the... 相似文献