In particular, when n=2 , we consider (Ω αβ ) and (J αβ ) as two polars on P 5 .
特别,当n=2时,视(Ωαβ)和(Jαβ)为P5中的两个配极,我们证明了:存在这两个配极的绝对形的交集和Lie’s圆的集合之间的一一对应,并且,两个Lie′s圆同向相切当且仅当它们在P5中的像点关于(Jαβ)彼此共轭,此外,P5中的射影变换G保持(Ωαβ)不变当且仅当G=∧,∈PGL(4,R),又如果G还保持(Jαβ)不变,则必∈PGsp(4)。
Thisarticle shows mainly that the two definitions are equal with Polarization.
圆锥曲线即二次曲线,它的中心、直径、渐近线等概念在欧氏平面解析几何中已给出过定义,在射影几何中又给出一种新定义,本文主要利用配极变换证明两种定义的等价性,并且举实例说明根据射影几何中的定又可找出较方便的计算公式。
The paper gives the condition of polarization established in four dimension and disease three types of involstory conespondence (point~point on a line;point~line ona plane; point~plane in a hyper-plane) derived from polarization in four dimension indetail.
本文在文献[1]的基础上,讨论了建立四维场配极对应的条件、四维场配极对应派生的直线上对合的点~点对应,平面上对合的点~线对应和超平面上对合的点~面对应,并详细讨论了四维场配极变换的基本作图。
This article tries to prove some theorems on polarization and hyperquadric, using correlation correspondential and polarizational projective geometric theories on n-dimensional projective Space.
本文利用n维射影空间的对射对应、配极对应等射影几何理论,推证出关于配极对应和二次超曲面的几个定理。
In this paper,the existence theorem of midpoint chord of quadratic curve,as well as its proof,is given via methods of projective geometry and polarity principle.
文章利用射影几何方法及配极原理给出二次曲线中点弦存在性定理的证明。
Some properties of projective transformation on projection plane producing by polar transformation;
配极变换诱导的直射变换的若干性质
This paper is gives a simplified formula of polar transformation in projective space pn and peints out its use.
给出了射影空间Pn中配极变换的一个化简公式并指出它的应用。
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