Differential Geometry in the Large (Record no. 31329)
[ view plain ]
| 000 -LEADER | |
|---|---|
| fixed length control field | 04222nam a22004935i 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783662215630 |
| -- | 978-3-662-21563-0 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.36 |
| 100 1# - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Hopf, Heinz. |
| 245 10 - TITLE STATEMENT | |
| Title | Differential Geometry in the Large |
| Sub Title | Seminar Lectures New York University 1946 and Stanford University 1956 / |
| Statement of responsibility, etc | by Heinz Hopf. |
| 260 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Berlin, Heidelberg : |
| Name of publisher | Springer Berlin Heidelberg : |
| -- | Imprint: Springer, |
| Year of publication | 1983. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | VII, 189 p. |
| Other physical details | online resource. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Lecture Notes in Mathematics, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Global differential geometry. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Topology. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Differential Geometry. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Topology. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | History and Philosophical Foundations of Physics. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-662-21563-0 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | E-BOOKS |
| 264 #1 - | |
| -- | Berlin, Heidelberg : |
| -- | Springer Berlin Heidelberg : |
| -- | Imprint: Springer, |
| -- | 1983. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 0075-8434 ; |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|
| IMSc Library | EBK2035 | http://dx.doi.org/10.1007/978-3-662-21563-0 | E-BOOKS |