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Berger, Marcel, Gostiaux, Bernard, Levy, Silvio:

Differential Geometry: Manifolds, Curves, and Surfaces. Graduate Texts in Mathematics 115 - edition reliée, livre de poche

1998, ISBN: 9780387966267

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Berger, Marcel, Gostiaux, Bernard, Levy, Silvio:

Differential Geometry: Manifolds, Curves, and Surfaces. Graduate Texts in Mathematics 115 - edition reliée, livre de poche

1990, ISBN: 9780387966267

Oxford - Cambridge - England: Basil Blackwell, Ltd, 1990. First Edition . Hard Back. As New/As New. 6 1/4" x 9 1/4. 334 Pages Indexed. As New with flawless interior text pages. T… Plus…

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Differential Geometry: Manifolds, Curves, and Surfaces Manifolds, Curves, and Surfaces - Berger, Marcel; Gostiaux, Bernard; Levy, Silvio (Übersetzung)
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Berger, Marcel; Gostiaux, Bernard; Levy, Silvio (Übersetzung):
Differential Geometry: Manifolds, Curves, and Surfaces Manifolds, Curves, and Surfaces - edition reliée, livre de poche

1987

ISBN: 0387966269

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Berger, Marcel, Gostiaux, Bernard:
Differential Geometry: Manifolds, Curves, and Surfaces (Graduate Texts in Mathematics) - edition reliée, livre de poche

1987, ISBN: 0387966269

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Berger, Marcel, Gostiaux, Bernard:
Differential Geometry: Manifolds, Curves, and Surfaces (Graduate Texts in Mathematics) - edition reliée, livre de poche

1987, ISBN: 0387966269

[EAN: 9780387966267], [PU: Springer], Befriedigend/Good: Durchschnittlich erhaltenes Buch bzw. Schutzumschlag mit Gebrauchsspuren, aber vollständigen Seiten. / Describes the average WORN … Plus…

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Détails sur le livre
Differential Geometry: Manifolds Curves and Surfaces

This book is an introduction to modern differential geometry. The authors begin with the necessary tools from analysis and topology, including Sard's theorem, de Rham cohomology, calculus on manifolds, and a degree theory. The general theory is illustrated and expanded using the examples of curves and surfaces. In particular, the book contains the classical local and global theory of surfaces, including the fundamental forms, curvature, the Gauss-Bonnet formula, geodesics, and minimal surfaces.

Informations détaillées sur le livre - Differential Geometry: Manifolds Curves and Surfaces


EAN (ISBN-13): 9780387966267
ISBN (ISBN-10): 0387966269
Version reliée
Livre de poche
Date de parution: 2007
Editeur: Springer New York
474 Pages
Poids: 0,888 kg
Langue: eng/Englisch

Livre dans la base de données depuis 2007-04-12T22:05:28+02:00 (Paris)
Page de détail modifiée en dernier sur 2024-03-03T15:58:17+01:00 (Paris)
ISBN/EAN: 0387966269

ISBN - Autres types d'écriture:
0-387-96626-9, 978-0-387-96626-7
Autres types d'écriture et termes associés:
Auteur du livre: gostiaux berger, marc bernard, marcel levy, berg, silvio bucher, lee, serge lang, geometry
Titre du livre: geometry old, differential geometry curves surfaces, res institution, manifolds and differential geometry, graduate texts mathematics


Données de l'éditeur

Auteur: Marcel Berger; Bernard Gostiaux
Titre: Graduate Texts in Mathematics; Differential Geometry: Manifolds, Curves, and Surfaces - Manifolds, Curves, and Surfaces
Editeur: Springer; Springer US
476 Pages
Date de parution: 1987-11-23
New York; NY; US
Traducteur: Silvio Levy
Poids: 1,900 kg
Langue: Anglais
96,29 € (DE)
98,99 € (AT)
106,50 CHF (CH)
POD
XII, 476 p.

BB; Differential Geometry; Hardcover, Softcover / Mathematik/Geometrie; Differentielle und Riemannsche Geometrie; Verstehen; Gaussian curvature; Mean curvature; Minimal surface; curvature; differential geometry; manifold; Differential Geometry; BC; EA

0. Background.- 0.0 Notation and Recap.- 0.1 Exterior Algebra.- 0.2 Differential Calculus.- 0.3 Differential Forms.- 0.4 Integration.- 0.5 Exercises.- 1. Differential Equations.- 1.1 Generalities.- 1.2 Equations with Constant Coefficients. Existence of Local Solutions.- 1.3 Global Uniqueness and Global Flows.- 1.4 Time- and Parameter-Dependent Vector Fields.- 1.5 Time-Dependent Vector Fields: Uniqueness And Global Flow.- 1.6 Cultural Digression.- 2. Differentiable Manifolds.- 2.1 Submanifolds of Rn.- 2.2 Abstract Manifolds.- 2.3 Differentiable Maps.- 2.4 Covering Maps and Quotients.- 2.5 Tangent Spaces.- 2.6 Submanifolds, Immersions, Submersions and Embeddings.- 2.7 Normal Bundles and Tubular Neighborhoods.- 2.8 Exercises.- 3. Partitions of Unity, Densities and Curves.- 3.1 Embeddings of Compact Manifolds.- 3.2 Partitions of Unity.- 3.3 Densities.- 3.4 Classification of Connected One-Dimensional Manifolds.- 3.5 Vector Fields and Differential Equations on Manifolds.- 3.6 Exercises.- 4. Critical Points.- 4.1 Definitions and Examples.- 4.2 Non-Degenerate Critical Points.- 4.3 Sard’s Theorem.- 4.4 Exercises.- 5. Differential Forms.- 5.1 The Bundle ?rT*X.- 5.2 Differential Forms on a Manifold.- 5.3 Volume Forms and Orientation.- 5.4 De Rham Groups.- 5.5 Lie Derivatives.- 5.6 Star-shaped Sets and Poincaré’s Lemma.- 5.7 De Rham Groups of Spheres and Projective Spaces.- 5.8 De Rham Groups of Tori.- 5.9 Exercises.- 6. Integration of Differential Forms.- 6.1 Integrating Forms of Maximal Degree.- 6.2 Stokes’ Theorem.- 6.3 First Applications of Stokes’ Theorem.- 6.4 Canonical Volume Forms.- 6.5 Volume of a Submanifold of Euclidean Space.- 6.6 Canonical Density on a Submanifold of Euclidean Space.- 6.7 Volume of Tubes I.- 6.8 Volume of Tubes II.- 6.9 Volume of Tubes III.- 6.10 Exercises.- 7. Degree Theory.- 7.1 Preliminary Lemmas.- 7.2 Calculation of Rd(X).- 7.3 The Degree of a Map.- 7.4 Invariance under Homotopy. Applications.- 7.5 Volume of Tubes and the Gauss-Bonnet Formula.- 7.6 Self-Maps of the Circle.- 7.7 Index of Vector Fields on Abstract Manifolds.- 7.8 Exercises.- 8. Curves: The Local Theory.- 8.0 Introduction.- 8.1 Definitions.- 8.2 Affine Invariants: Tangent, Osculating Plan, Concavity.- 8.3 Arclength.- 8.4 Curvature.- 8.5 Signed Curvature of a Plane Curve.- 8.6 Torsion of Three-Dimensional Curves.- 8.7 Exercises.- 9. Plane Curves: The Global Theory.- 9.1 Definitions.- 9.2 Jordan’s Theorem.- 9.3 The Isoperimetric Inequality.- 9.4 The Turning Number.- 9.5 The Turning Tangent Theorem.- 9.6 Global Convexity.- 9.7 The Four-Vertex Theorem.- 9.8 The Fabricius-Bjerre-Halpern Formula.- 9.9 Exercises.- 10. A Guide to the Local Theory of Surfaces in R3.- 10.1 Definitions.- 10.2 Examples.- 10.3 The Two Fundamental Forms.- 10.4 What the First Fundamental Form Is Good For.- 10.5 Gaussian Curvature.- 10.6 What the Second Fundamental Form Is Good For.- 10.7 Links Between the two Fundamental Forms.- 10.8 A Word about Hypersurfaces in Rn+1.- 11. A Guide to the Global Theory of Surfaces.- 11.1 Shortest Paths.- 11.2 Surfaces of Constant Curvature.- 11.3 The Two Variation Formulas.- 11.4 Shortest Paths and the Injectivity Radius.- 11.5 Manifolds with Curvature Bounded Below.- 11.6 Manifolds with Curvature Bounded Above.- 11.7 The Gauss-Bonnet and Hopf Formulas.- 11.8 The Isoperimetric Inequality on Surfaces.- 11.9 Closed Geodesics and Isosystolic Inequalities.- 11.10 Surfaces AU of Whose Geodesics Are Closed.- 11.11 Transition: Embedding and Immersion Problems.- 11.12 Surfaces of Zero Curvature.- 11.13 Surfaces of Non-Negative Curvature.- 11.14 Uniqueness and Rigidity Results.- 11.15 Surfaces of Negative Curvature.- 11.16 Minimal Surfaces.- 11.17 Surfaces of Constant Mean Curvature, or Soap Bubbles.- 11.18 Weingarten Surfaces.- 11.19 Envelopes of Families of Planes.- 11.20 Isoperimetric Inequalities for Surfaces.- 11.21 A Pot-pourri of Characteristic Properties.- Index of Symbols and Notations.

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