株式会社極東書店トップ ＞ 商品一覧 ＞ The Laplacian on a Riemannian Manifold : An Introduction to Analysis on Manifolds.
商品詳細
The Laplacian on a Riemannian Manifold : An Introduction to Analysis on Manifolds.
・ISBN 978-0-521-46300-3 hard GB£ 121.00
￥38,332.- (税込) ※（※）価格はご注文時の参考価格となります。
納品価格につきましては書籍の入荷時点で確定となります。
版元の原価改定、外国為替の変動等により異なる場合がございますので、予めご了承下さい。
お気に入り
★★★
電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-0-511-62378-3
| 著者・編者 | Rosenberg, Steven, |
|---|---|
| シリーズ | London Mathematical Society Student Texts |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 1997 |
| ページ数 | 188 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-10593＞ |
解説
This text on analysis of 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 associated 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 Atiyah-Singer index theorem and its applications are developed (without complete proofs) via the heat equation method. Zeta functions for Laplacians and analytic torsion are also treated, and the recently uncovered relation between index theory and analytic torsion is laid out. The text is aimed at students who have had a first course in differentiable manifolds, and the Riemannian geometry used is developed from the beginning. There are over 100 exercises with hints.