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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).
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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).
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Global Differential Geometry of Surfaces
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Global Differential Geometry of Surfaces
Verlag:
Springer Netherlands, Springer Netherlands Nov 2001, 2001
ISBN 10: 1402003188
ISBN 13: 9781402003189
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Taschenbuch. Zustand: Neu. 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 156 pp. Englisch. Artikel-Nr. 9781402003189
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Global Differential Geometry of Surfaces
Verlag:
Springer Netherlands, Springer Netherlands, 2001
ISBN 10: 1402003188
ISBN 13: 9781402003189
Neu
Taschenbuch
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Taschenbuch. Zustand: Neu. 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). Artikel-Nr. 9781402003189
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