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	Laguerre geometry of surfaces in R-3
	Li, TZ
	2005
关键词	Laguerre transformation Laguerre Gauss map Laguerre minimal surface S-N
英文摘要	Let f : M -> R-3 be an oriented surface with non-degenerate second fundamental form. We denote by H and K its mean curvature and Gauss curvature. Then the Laguerre volume of f, defined by L(f) = f (H-2 - K)/KdM, is an invariant under the Laguerre transformations. The critical surfaces of the functional L are called Laguerre minimal surfaces. In this paper we study the Laguerre minimal surfaces in R-3 by using the Laguerre Gauss map. It is known that a generic Laguerre minimal surface has a dual Laguerre minimal surface with the same Gauss map. In this paper we show that any surface which is not Laguerre minimal is uniquely determined by its Laguerre Gauss map. We show also that round spheres are the only compact Laguerre minimal surfaces in R-3. And we give a classification theorem of surfaces in R-3 with vanishing Laguerre form.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000236388600030&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics, Applied; Mathematics; SCI(E); 中国科技核心期刊(ISTIC); 中国科学引文数据库(CSCD); 16; ARTICLE; 6; 1525-1534; 21
语种	英语
出处	SCI
出版者	acta mathematica sinica english series
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157944]
专题	数学科学学院
推荐引用方式 GB/T 7714	Li, TZ. Laguerre geometry of surfaces in R-3. 2005-01-01.

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