Isometric embedding of Riemannian manifolds in Euclidean spaces

＜Book＞
Isometric embedding of Riemannian manifolds in Euclidean spaces

Responsibility	Qing Han, Jia-Xing Hong
Series	Mathematical surveys and monographs ; v. 130
Material Type	Book
Publication	Providence, R.I. : American Mathematical Society , c2006
Language	English
Size	xiv, 260 p. : ill. ; 26 cm
Abstract	This is a systematic presentation of results concerning the isometric embedding of Riemannian manifolds in local and global Euclidean spaces, especially focused on the isometric embedding of surfaces ...n a Euclidean space R3 and primarily employing partial differential equation techniques for proving results. The authors begin their treatment with discussion of fundamental results of the isometric embedding of Riemannian manifolds in Euclidean spaces, including the Janet-Cartan Theorem and Nash Embedding Theorem. Next, looking at the local isometric embedding of surfaces in R3, they discuss metrics with Gauss curvature that is everywhere positive, negative, nonnegative, nonpositive, as well as the case of the mixed sign. Finally, the explore the global isometric embedding of surfaces in R3, focusing on metrics on S2 with positive Gauss curvature and complete metrics in R2 with negative Gauss curvature. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com) show more
Electronic Version	https://hdl.handle.net/2324/6947479

Status	Volume	Location	Call No.	Printed	Collection Name	Barcode No.	Comments	Reserve	Copy	Automatic archive
		SciTech 3F Mathematical Books	HAN,/10/2	2006		023212006005017		Reserve			Reserve

Notes	Includes bibliographical references (p. 249-257) and index
Authors	*Han, Qing Hong, Jia-Xing, 1942-
Subjects	LCSH:Riemannian manifolds LCSH:Isometrics (Mathematics) LCSH:Algebraic spaces
Classification	LCC:QA649 DC22:516.3/62
ID	1001240282
ISBN	0821840711
NCID	BA78836447
Vol	ISBN:0821840711 ; XISBN:9780821840719
Created Date	2009.09.18
Modified Date	2017.02.18