<電子ブック>
Differential Geometry in the Large : Seminar Lectures New York University 1946 and Stanford University 1956 / by Heinz Hopf
(Lecture Notes in Mathematics. ISSN:16179692 ; 1000)
版 | 1st ed. 1983. |
---|---|
出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 1983 |
大きさ | VII, 189 p : online resource |
著者標目 | *Hopf, Heinz author SpringerLink (Online service) |
件 名 | LCSH:Geometry, Differential LCSH:Topology LCSH:Physics—Philosophy FREE:Differential Geometry FREE:Topology FREE:Philosophical Foundations of Physics and Astronomy |
一般注記 | One Selected Topics in Geometry -- I The Euler Characteristic and Related Topics -- II Selected Topics in Elementary Differential Geometry -- III The Isoperimetric Inequality and Related Inequalities -- IV The Elementary Concept of Area and Volume -- Two Differential Geometry in the Large -- I Differential Geometry of Surfacesin the Small -- II Some General Remarks on Closed Surfaces in Differential Geometry -- III The Total Curvature (Curvatura Integra) of a Closed Surface with Riemannian Metric and Poincaré’s Theorem on the Singularities of Fields of Line Elements -- IV Hadamard’s Characterization of the Ovaloids -- V Closed Surfaces with Constant Gauss Curvature (Hilbert’s Methods) — Generalizations and Problems — General Remarks on Weingarten Surfaces -- VI General Closed Surfaces of Genus O with Constant Mean Curvature — Generalizations -- VII Simple Closed Surfaces (of Arbitrary Genus) with Constant Mean Curvature — Generalizations -- VIII The Congruence Theorem for Ovaloids -- IX Singularities of Surfaces with Constant Negative Gauss Curvature These notes consist of two parts: 1) Selected Topics in Geometry, New York University 1946, Notes by Peter Lax. 2) Lectures on Differential Geometry in the Large, Stanford University 1956, Notes by J. W. Gray. They are reproduced here with no essential change. Heinz Hopf was a mathematician who recognized important mathema tical ideas and new mathematical phenomena through special cases. In the simplest background the central idea or the difficulty of a problem usually becomes crystal clear. Doing geometry in this fashion is a joy. Hopf's great insight allows this approach to lead to serious ma thematics, for most of the topics in these notes have become the star ting-points of important further developments. I will try to mention a few. It is clear from these notes that Hopf laid the emphasis on poly hedral differential geometry. Most of the results in smooth differen tial geometry have polyhedral counterparts, whose understanding is both important and challenging. Among recent works I wish to mention those of Robert Connelly on rigidity, which is very much in the spirit of these notes (cf. R. Connelly, Conjectures and open questions in ri gidity, Proceedings of International Congress of Mathematicians, Hel sinki 1978, vol. 1, 407-414 ) • A theory of area and volume of rectilinear'polyhedra based on de compositions originated with Bolyai and Gauss HTTP:URL=https://doi.org/10.1007/978-3-662-21563-0 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9783662215630 |
|
電子リソース |
|
EB00209310 |
類似資料
この資料の利用統計
このページへのアクセス回数:7回
※2017年9月4日以降