Global Differential Geometry of Surfaces

A. Svec

ISBN 10: 9027712956 / ISBN 13: 9789027712950

Editore: Springer Netherlands, Springer Netherlands Feb 1982, 1982

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Neuware -Writing this book, I had in my mind areader trying to get some knowledge of a part of the modern differential geometry. I concentrate myself on the study of sur faces in the Euclidean 3-space, this being the most natural object for investigation. The global differential geometry of surfaces in E3 is based on two classical results: (i) the ovaloids (i.e., closed surfaces with positive Gauss curvature) with constant Gauss or mean curvature are the spheres, (ü) two isometrie ovaloids are congruent. The results presented here show vast generalizations of these facts. Up to now, there is only one book covering this area of research: the Lecture Notes [3] written in the tensor slang. In my book, I am using the machinary of E. Cartan's calculus. It should be equivalent to the tensor calculus; nevertheless, using it I get better results (but, honestly, sometimes it is too complicated). It may be said that almost all results are new and belong to myself (the exceptions being the introductory three chapters, the few classical results and results of my post graduate student Mr. M. ÄFWAT who proved Theorems V.3.1, V.3.3 and VIII.2.1-6).Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 160 pp. Englisch.

Codice articolo 9789027712950

Dati bibliografici

• Titolo: Global Differential Geometry of Surfaces
• Editore: Springer Netherlands, Springer Netherlands Feb 1982
• Data di pubblicazione: 1982
• Lingua: Inglese
• ISBN 10: 9027712956
• ISBN 13: 9789027712950
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 14 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 14 millimetri di profondità
• Peso: 412 grammi

Descrizione articolo

Riassunto

Writing this book, I had in my mind areader trying to get some knowledge of a part of the modern differential geometry. I concentrate myself on the study of sur­ faces in the Euclidean 3-space, this being the most natural object for investigation. The global differential geometry of surfaces in E3 is based on two classical results: (i) the ovaloids (i.e., closed surfaces with positive Gauss curvature) with constant Gauss or mean curvature are the spheres, (ü) two isometrie ovaloids are congruent. The results presented here show vast generalizations of these facts. Up to now, there is only one book covering this area of research: the Lecture Notes [3] written in the tensor slang. In my book, I am using the machinary of E. Cartan's calculus. It should be equivalent to the tensor calculus; nevertheless, using it I get better results (but, honestly, sometimes it is too complicated). It may be said that almost all results are new and belong to myself (the exceptions being the introductory three chapters, the few classical results and results of my post­ graduate student Mr. M. ÄFWAT who proved Theorems V.3.1, V.3.3 and VIII.2.1-6).

Contenuti

I. Multilinear algebra.- II. Differentiable manifolds.- III. Methods of global differential geometry.- IV. Local differential geometry of surfaces in E3.- V. Global differential geometry of Weingarten surfaces.- VI. Global differential geometry of isometries.- VII. Surfaces in E4 and E5.- VIII. Global differential geometry of hypersurfaces in En+1.