omitir hasta el contenido
Differential geometry : Manifolds, curves, and surfaces Ver este material de antemano
CerrarVer este material de antemano
Chequeando…

Differential geometry : Manifolds, curves, and surfaces

Autor: Marcel Berger; Bernard Gostiaux; Silvio Levy
Editorial: Heidelberg [etc.] : Springer-Verlag ; New York ; Berlin, cop.1988.
Serie: Graduate texts in mathematics.
Edición/Formato:   Libro : Inglés (eng)Ver todas las ediciones y todos los formatos
Base de datos:WorldCat
Resumen:

Presents an introduction to modern differential geometry. This book features tools from analysis and topology, including Sard's theorem, de Rham cohomology, calculus on manifolds, and a degree theory.  Leer más

Calificación:

(todavía no calificado) 0 con reseñas - Ser el primero.

Temas
Más materiales como éste

 

Encontrar un ejemplar en la biblioteca

&AllPage.SpinnerRetrieving; Encontrando bibliotecas que tienen este material…

Detalles

Género/Forma: [manuel]
Tipo de documento: Libro/Texto
Todos autores / colaboradores: Marcel Berger; Bernard Gostiaux; Silvio Levy
ISBN: 0387966269 9780387966267 3540966269 9783540966265
Número OCLC: 491131246
Notas: Traduit de : "Géométrie différentielle : variétés, courbes et surfaces"
Descripción: 1 vol. (XII-474 p.) ; 25 cm.
Contenido: 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 Poincare'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.
Título de la serie: Graduate texts in mathematics.
Responsabilidad: Marcel Berger, Bernard Gostiaux ; translated from the French by Silvio Levy.
Más información:

Reseñas

Reseñas contribuidas por usuarios
Recuperando reseñas de GoodReads…
Recuperando reseñas de DOGObooks…

Etiquetas

Ser el primero.
Confirmar este pedido

Ya ha pedido este material. Escoja OK si desea procesar el pedido de todos modos.

Datos enlazados


<http://www.worldcat.org/oclc/491131246>
bgn:translationOfWork
library:oclcnum"491131246"
library:placeOfPublication
library:placeOfPublication
library:placeOfPublication
library:placeOfPublication
rdf:typeschema:Book
schema:about
schema:about
schema:about
schema:about
schema:about
schema:about
schema:about
schema:about
schema:about
schema:about
schema:about
schema:contributor
schema:contributor
schema:copyrightYear"op.1"
schema:creator
schema:datePublished"1988"
schema:exampleOfWork<http://worldcat.org/entity/work/id/1103195731>
schema:inLanguage"en"
schema:isPartOf
schema:name"Differential geometry Manifolds, curves, and surfaces"
schema:publication
schema:publisher
schema:workExample
schema:workExample
wdrs:describedby

Content-negotiable representations

Cerrar ventana

Inicie una sesión con WorldCat 

¿No tienes una cuenta? Puede fácilmente crear una cuenta gratuita.