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Titlebook: Differential Geometry in the Large; Seminar Lectures New Heinz Hopf Book 19831st edition Springer-Verlag Berlin Heidelberg 1983 Geometrie.G

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樓主
發(fā)表于 2025-3-21 16:43:58 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Differential Geometry in the Large
副標題Seminar Lectures New
編輯Heinz Hopf
視頻videohttp://file.papertrans.cn/279/278761/278761.mp4
叢書名稱Lecture Notes in Mathematics
圖書封面Titlebook: Differential Geometry in the Large; Seminar Lectures New Heinz Hopf Book 19831st edition Springer-Verlag Berlin Heidelberg 1983 Geometrie.G
描述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 Internationa
出版日期Book 19831st edition
關鍵詞Geometrie; Geometry; Globale Differentialgeometrie; curvature; differential geometry; Gaussian curvature;
版次1
doihttps://doi.org/10.1007/978-3-662-21563-0
isbn_ebook978-3-662-21563-0Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag Berlin Heidelberg 1983
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沙發(fā)
發(fā)表于 2025-3-21 21:34:20 | 只看該作者
0075-8434 onnelly on rigidity, which is very much in the spirit of these notes (cf. R. Connelly, Conjectures and open questions in ri- gidity, Proceedings of Internationa978-3-662-21563-0Series ISSN 0075-8434 Series E-ISSN 1617-9692
板凳
發(fā)表于 2025-3-22 01:20:46 | 只看該作者
地板
發(fā)表于 2025-3-22 07:57:21 | 只看該作者
https://doi.org/10.1007/978-3-642-98032-9onvex set with a non-empty interior. It is easy to show that a convex body is homeomorphic to a solid sphere (but we will not need this fact). In these notes we will assume in addition that the boundary surface of a convex body in E. is several times differentiable.
5#
發(fā)表于 2025-3-22 10:01:01 | 只看該作者
Hadamard’s Characterization of the Ovaloidsonvex set with a non-empty interior. It is easy to show that a convex body is homeomorphic to a solid sphere (but we will not need this fact). In these notes we will assume in addition that the boundary surface of a convex body in E. is several times differentiable.
6#
發(fā)表于 2025-3-22 14:11:31 | 只看該作者
7#
發(fā)表于 2025-3-22 18:11:00 | 只看該作者
https://doi.org/10.1007/978-3-642-98032-9onvex set with a non-empty interior. It is easy to show that a convex body is homeomorphic to a solid sphere (but we will not need this fact). In these notes we will assume in addition that the boundary surface of a convex body in E. is several times differentiable.
8#
發(fā)表于 2025-3-23 00:27:18 | 只看該作者
,Mittel zur Steigerung der Abwehrkr?fte,nstant mean curvature H. We will actually prove the stronger result that if the principle curvatures k. and k. of an ovaloid satisfy a relationship k. = f(k.) where f is a decreasing function, then the ovaloid is a sphere. Since K = k.k. and ., the two results, 1) and 2) stated above will follows Ir
9#
發(fā)表于 2025-3-23 02:06:56 | 只看該作者
10#
發(fā)表于 2025-3-23 09:04:46 | 只看該作者
John Rooksby,Ian Sommerville,Mike PiddThe first topic to be discussed will be Euler’s famous relation between the number of faces, edges and vertices of a convex polyhedron.
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