Global Differential Geometry of Surfaces

A. Svec

ISBN 10: 9027712956 / ISBN 13: 9789027712950

Edité par Springer Netherlands, Springer Netherlands, 1982

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 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).

N° de réf. du vendeur 9789027712950

Détails bibliographiques

• Titre: Global Differential Geometry of Surfaces
• Éditeur: Springer Netherlands, Springer Netherlands
• Date de parution: 1982
• Langue: anglais
• ISBN à 10 chiffres: 9027712956
• ISBN à 13 chiffres: 9789027712950
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 14 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 14 millimètres de profondeur
• Poids: 412 grammes

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Synopsis

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).