The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds

＜図書＞
The Laplacian on a Riemannian manifold : an introduction to analysis on manifolds

責任表示	Steven Rosenberg
シリーズ	London Mathematical Society student texts ; 31
データ種別	図書
出版情報	New York ; Cambridge : Cambridge University Press , 1997
本文言語	英語
大きさ	x, 172 p. : ill. ; 24 cm
概要	This text on analysis on Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow assoc...ated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The author develops the Atiyah-Singer index theorem and its applications (without complete proofs) via the heat equation method. Rosenberg also treats zeta functions for Laplacians and analytic torsion, and lays out the recently uncovered relation between index theory and analytic torsion. The text is aimed at students who have had a first course in differentiable manifolds, and the author develops the Riemannian geometry used from the beginning. There are over 100 exercises with hints. This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.続きを見る
電子版へのリンク	https://hdl.handle.net/2324/7015891

巻次	所蔵場所	請求記号	刷年	資料番号	予約・取寄
: hdc	理系図1F 開架	414.81/R 72	1998	003212007001116	予約・取寄	予約・取寄
: hdc	理系図3F 数理独自	ROSE/85/1	1997	023211997002530	予約・取寄	予約・取寄
: pbk	数理数理科学	ROSE/85/1A	1998	033212015500187	リコール	リコール

一般注記	Reprinted 1998: x, 174 p., bibliography (p. 167-171) Includes bibliographical references (p. 165-169) and index
著者標目	*Rosenberg, Steven, 1951-
件　名	LCSH:Riemannian manifolds LCSH:Laplacian operator
分　類	LCC:QA649 DC20:516.3/73 NDC8:414.81
書誌ID	1001058730
ISBN	9780521463003
NCID	BA29120482
巻冊次	: hdc ; ISBN:9780521463003 ; XISBN:0521463009 : pbk ; ISBN:9780521468312 ; XISBN:0521468310
登録日	2009.09.17
更新日	2017.02.18