Riemannian geometry of noncommutative surfaces

doi:10.1063/1.2953461

CSpace

	Riemannian geometry of noncommutative surfaces
	Chaichian, M.1,2; Tureanu, A.1,2; Zhang, R. B.3; Zhang, Xiao 4
	2008-07-01
发表期刊	JOURNAL OF MATHEMATICAL PHYSICS
ISSN	0022-2488
卷号	49 期号:7 页码:26
摘要	A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step toward the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the underlying structure of Einstein's theory of general relativity and led to further developments of the latter. The notions of metric and connections on such noncommutative surfaces are introduced, and it is shown that the connections are metric compatible, giving rise to the corresponding Riemann curvature. The latter also satisfies the noncommutative analog of the first and second Bianchi identities. As examples, noncommutative analogs of the sphere, torus, and hyperboloid are studied in detail. The problem of covariance under appropriately defined general coordinate transformations is also discussed and commented on as compared to other treatments. (C) 2008 American Institute of Physics.
DOI	10.1063/1.2953461
语种	英语
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000258175300025
出版者	AMER INST PHYSICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5780
专题	中国科学院数学与系统科学研究院
通讯作者	Chaichian, M.
作者单位	1.Univ Helsinki, Dept Phys Sci, FIN-00014 Helsinki, Finland 2.Helsinki Inst Phys, FIN-00014 Helsinki, Finland 3.Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia 4.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Chaichian, M.,Tureanu, A.,Zhang, R. B.,et al. Riemannian geometry of noncommutative surfaces[J]. JOURNAL OF MATHEMATICAL PHYSICS,2008,49(7):26.
APA	Chaichian, M.,Tureanu, A.,Zhang, R. B.,&Zhang, Xiao.(2008).Riemannian geometry of noncommutative surfaces.JOURNAL OF MATHEMATICAL PHYSICS,49(7),26.
MLA	Chaichian, M.,et al."Riemannian geometry of noncommutative surfaces".JOURNAL OF MATHEMATICAL PHYSICS 49.7(2008):26.