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	Rigid geometric structures, isometric actions, and algebraic quotients
	An, Jinpeng
	2012
关键词	Rigid geometric structure Isometric action Invariant measure Fundamental group Algebraic quotient TRANSFORMATION GROUPS INVARIANT-MEASURES SUBGROUPS AUTOMORPHISM
英文摘要	By using a Borel density theorem for algebraic quotients, we prove a theorem concerning isometric actions of a Lie group G on a smooth or analytic manifold M with a rigid A-structure sigma. It generalizes Gromov's centralizer and representation theorems to the case where R(G) is split solvable and G/R(G) has no compact factors, strengthens a special case of Gromov's open dense orbit theorem, and implies that for smooth M and simple G, if Gromov's representation theorem does not hold, then the local Killing fields on (M) over tilde are highly non-extendable. As applications of the generalized centralizer and representation theorems, we prove (1) a structural property of Iso(M) for simply connected compact analytic M with unimodular sigma, (2) three results illustrating the phenomenon that if G is split solvable and large then pi(1)(M) is also large, and (3) two fixed point theorems for split solvable G and compact analytic M with non-unimodular sigma.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000301703400006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics; SCI(E); 0; ARTICLE; 1; 153-185; 157
语种	英语
出处	SCI
出版者	geometriae dedicata
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157541]
专题	数学科学学院
推荐引用方式 GB/T 7714	An, Jinpeng. Rigid geometric structures, isometric actions, and algebraic quotients. 2012-01-01.

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