Closed form of the inverse Plucker correspondence in line geometry

doi:10.1007/s11425-017-9242-3

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	Closed form of the inverse Plucker correspondence in line geometry
	Dong, Lei; Li, Hongbo; Huang, Lei; Shao, Changpeng
	2019-12-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	62 期号:12 页码:2617-2630
摘要	By mapping the homogeneous coordinates of two points in space to the Plucker coordinates of the line they determine, any transformation of type SL(4) upon points in space is mapped to a transformation of type SO0(3, 3), the latter being the connected component containing the identity of the special orthogonal transformation group of the linear space spanned by Plucker coordinates. This is the classical Plucker correspondence, two-to-one and onto. It has important applications in line geometry and projective transformations. While the explicit form of Plucker correspondence is trivial to present, its inverse in explicit form, which is also important in application, is not found in the literature. In this paper, we present a simple and unified formula for the inverse of the Plucker correspondence.
关键词	Plucker correspondence inverse Plucker correspondence line geometry SL(4) SO(3,3)
DOI	10.1007/s11425-017-9242-3
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11671388] ; CAS Frontier Key Project[QYZDJ-SSW-SYS022]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000509102200012
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50552
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Hongbo
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Dong, Lei,Li, Hongbo,Huang, Lei,et al. Closed form of the inverse Plucker correspondence in line geometry[J]. SCIENCE CHINA-MATHEMATICS,2019,62(12):2617-2630.
APA	Dong, Lei,Li, Hongbo,Huang, Lei,&Shao, Changpeng.(2019).Closed form of the inverse Plucker correspondence in line geometry.SCIENCE CHINA-MATHEMATICS,62(12),2617-2630.
MLA	Dong, Lei,et al."Closed form of the inverse Plucker correspondence in line geometry".SCIENCE CHINA-MATHEMATICS 62.12(2019):2617-2630.