FUNDAMENTAL THEOREM OF GEOMETRY WITHOUT THE SURJECTIVE ASSUMPTION

doi:10.1090/tran/6533

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	FUNDAMENTAL THEOREM OF GEOMETRY WITHOUT THE SURJECTIVE ASSUMPTION
	Li, Baokui 1,2; Wang, Yuefei3
	2016-10-01
发表期刊	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN	0002-9947
卷号	368 期号:10 页码:6819-6834
摘要	In this paper, we solve the rigidity problem on geodesic maps in the hyperbolic space. The main result is that a geodesic-to-geodesic injection in hyperbolic space D-n is an isometry or a composition of an isometry and an affine transformation under the Klein model if and only if it is non-degenerate. We first solve the rigidity problems on Euclidean space and the n-sphere and show that a line-to-line injection in Euclidean space R-n is an affine transformation if and only if it is non-degenerate and that a circle-to-circle injection on the n-sphere R-n is a Mobius transformation if and only if it is non-degenerate. More general results for hyperplane-to-hyperplane maps are obtained. The key method is to establish a new version of the celebrated Pappas' Theorem.
关键词	Line-to-line transformations Pappus' Theorem g-reflections affine transformations Mobius transformations
DOI	10.1090/tran/6533
语种	英语
资助项目	NSF of China[11101032] ; NSF of China[10831004]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000372533200002
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22425
专题	数学所
通讯作者	Li, Baokui; Wang, Yuefei
作者单位	1.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China 2.Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 100081, Peoples R China 3.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Baokui,Wang, Yuefei. FUNDAMENTAL THEOREM OF GEOMETRY WITHOUT THE SURJECTIVE ASSUMPTION[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2016,368(10):6819-6834.
APA	Li, Baokui,&Wang, Yuefei.(2016).FUNDAMENTAL THEOREM OF GEOMETRY WITHOUT THE SURJECTIVE ASSUMPTION.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,368(10),6819-6834.
MLA	Li, Baokui,et al."FUNDAMENTAL THEOREM OF GEOMETRY WITHOUT THE SURJECTIVE ASSUMPTION".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 368.10(2016):6819-6834.