Normal view MARC view ISBD view

Introduction to Riemannian manifolds / John M. Lee.

By: Lee, John M, 1950-.
Material type: materialTypeLabelBookPublisher: New York, NY : Springer Berlin Heidelberg, 2018Edition: 2nd ed.Description: xiii, 437 p. il. 24 cm.Content type: text Media type: unmediated Carrier type: volumeISBN: 9783319917542.Other classification: 53-01 (53B20 53B30 53C20 53C21)
Contents:
1 What Is Curvature? [1] -- The Euclidean Plane [1] -- Surfaces in Space [4] -- Curvature in Higher Dimensions [7] -- 2 Riemannian Metrics [9] -- Definitions [9] -- Methods for Constructing Riemannian Metrics [15] -- Basic Constructions on Riemannian Manifolds [25] -- Lengths and Distances [33] -- Pseudo-Riemannian Metrics [40] -- Other Generalizations of Riemannian Metrics [46] -- Problems [47] -- 3 Model Riemannian Manifolds [55] -- Symmetries of Riemannian Manifolds [55] -- Euclidean Spaces [57] -- Spheres [58] -- Hyperbolic Spaces [62] -- Invariant Metrics on Lie Groups [67] -- Other Homogeneous Riemannian Manifolds [72] -- Model Pseudo-Riemannian Manifolds [79] -- Problems [80] -- 4 Connections [85] -- The Problem of Differentiating Vector Fields [85] -- Connections [88] -- Covariant Derivatives of Tensor Fields [95] -- Vector and Tensor Fields Along Curves [100] -- Geodesics [103] -- Parallel Transport [105] -- Pullback Connections [110] -- Problems [111] -- 5 The Levi-Civita Connection [115] -- The Tangential Connection Revisited [115] -- Connections on Abstract Riemannian Manifolds [117] -- The Exponential Map [126] -- Normal Neighborhoods and Normal Coordinates [131] -- Tubular Neighborhoods and Fermi Coordinates [133] -- Geodesics of the Model Spaces [136] -- Euclidean and Non-Euclidean Geometries [142] -- Problems [145] -- 6 Geodesics and Distance [151] -- Geodesics and Minimizing Curves [151] -- Uniformly Normal Neighborhoods [163] -- Completeness [166] -- Distance Functions [174] -- Semigeodesic Coordinates [181] -- Problems [185] -- 7 Curvature [193] -- Local Invariants [193] -- The Curvature Tensor [196] -- Flat Manifolds [199] -- Symmetries of the Curvature Tensor [202] -- The Ricci Identities [205] -- Ricci and Scalar Curvatures [207] -- The Weyl Tensor [212] -- Curvatures of Conformally Related Metrics [216] -- Problems [222] -- 8 Riemannian Submanifolds [225] -- The Second Fundamental Form [225] -- Hypersurfaces [234] -- Hypersurfaces in Euclidean Space [244] -- Sectional Curvatures [250] -- Problems [255] -- 9 The Gauss-Bonnet Theorem [263] -- Some Plane Geometry [263] -- The Gauss-Bonnet Formula [271] -- The Gauss-Bonnet Theorem [276] -- Problems [281] -- 10 Jacobi Fields [283] -- The Jacobi Equation [284] -- Basic Computations with Jacobi Fields [287] -- Conjugate Points [297] -- The Second Variation Formula [300] -- Cut Points [307] -- Problems [313] -- 11 Comparison Theory [319] -- Jacobi Fields, Hessians, and Riccati Equations [320] -- Comparisons Based on Sectional Curvature [327] -- Comparisons Based on Ricci Curvature [336] -- Problems [342] -- 12 Curvature and Topology [345] -- Manifolds of Constant Curvature [345] -- Manifolds of Nonpositive Curvature [352] -- Manifolds of Positive Curvature [361] -- Problems [368] -- Appendix A: Review of Smooth Manifolds [371] -- Topological Preliminaries [371] -- Smooth Manifolds and Smooth Maps [374] -- Tangent Vectors [376] -- Submanifolds [378] -- Vector Bundles [382] -- The Tangent Bundle and Vector Fields [384] -- Smooth Covering Maps [388] -- Appendix B: Review of Tensors [391] -- Tensors on a Vector Space [391] -- Tensor Bundles and Tensor Fields [396] -- Differential Forms and Integration [400] -- Densities [405] -- Appendix C: Review of Lie Groups [407] -- Definitions and Properties [407] -- The Lie Algebra of a Lie Group [408] -- Group Actions on Manifolds [411] -- References [415] -- Notation Index [419] -- Subject Index [423] --
List(s) this item appears in: ÚLTIMOS LIBROS INCORPORADOS
Tags from this library: No tags from this library for this title. Log in to add tags.
    average rating: 0.0 (0 votes)
Item type Home library Shelving location Call number Status Date due Barcode
Libros Libros Instituto de Matemática, CONICET-UNS
Últimas adquisiciones 53 L477 (Browse shelf) Available A-9298

Originally published with the title 'Riemannian manifolds: an introduction to curvature' in 1997.

1 What Is Curvature? [1] --
The Euclidean Plane [1] --
Surfaces in Space [4] --
Curvature in Higher Dimensions [7] --
2 Riemannian Metrics [9] --
Definitions [9] --
Methods for Constructing Riemannian Metrics [15] --
Basic Constructions on Riemannian Manifolds [25] --
Lengths and Distances [33] --
Pseudo-Riemannian Metrics [40] --
Other Generalizations of Riemannian Metrics [46] --
Problems [47] --
3 Model Riemannian Manifolds [55] --
Symmetries of Riemannian Manifolds [55] --
Euclidean Spaces [57] --
Spheres [58] --
Hyperbolic Spaces [62] --
Invariant Metrics on Lie Groups [67] --
Other Homogeneous Riemannian Manifolds [72] --
Model Pseudo-Riemannian Manifolds [79] --
Problems [80] --
4 Connections [85] --
The Problem of Differentiating Vector Fields [85] --
Connections [88] --
Covariant Derivatives of Tensor Fields [95] --
Vector and Tensor Fields Along Curves [100] --
Geodesics [103] --
Parallel Transport [105] --
Pullback Connections [110] --
Problems [111] --
5 The Levi-Civita Connection [115] --
The Tangential Connection Revisited [115] --
Connections on Abstract Riemannian Manifolds [117] --
The Exponential Map [126] --
Normal Neighborhoods and Normal Coordinates [131] --
Tubular Neighborhoods and Fermi Coordinates [133] --
Geodesics of the Model Spaces [136] --
Euclidean and Non-Euclidean Geometries [142] --
Problems [145] --
6 Geodesics and Distance [151] --
Geodesics and Minimizing Curves [151] --
Uniformly Normal Neighborhoods [163] --
Completeness [166] --
Distance Functions [174] --
Semigeodesic Coordinates [181] --
Problems [185] --
7 Curvature [193] --
Local Invariants [193] --
The Curvature Tensor [196] --
Flat Manifolds [199] --
Symmetries of the Curvature Tensor [202] --
The Ricci Identities [205] --
Ricci and Scalar Curvatures [207] --
The Weyl Tensor [212] --
Curvatures of Conformally Related Metrics [216] --
Problems [222] --
8 Riemannian Submanifolds [225] --
The Second Fundamental Form [225] --
Hypersurfaces [234] --
Hypersurfaces in Euclidean Space [244] --
Sectional Curvatures [250] --
Problems [255] --
9 The Gauss-Bonnet Theorem [263] --
Some Plane Geometry [263] --
The Gauss-Bonnet Formula [271] --
The Gauss-Bonnet Theorem [276] --
Problems [281] --
10 Jacobi Fields [283] --
The Jacobi Equation [284] --
Basic Computations with Jacobi Fields [287] --
Conjugate Points [297] --
The Second Variation Formula [300] --
Cut Points [307] --
Problems [313] --
11 Comparison Theory [319] --
Jacobi Fields, Hessians, and Riccati Equations [320] --
Comparisons Based on Sectional Curvature [327] --
Comparisons Based on Ricci Curvature [336] --
Problems [342] --
12 Curvature and Topology [345] --
Manifolds of Constant Curvature [345] --
Manifolds of Nonpositive Curvature [352] --
Manifolds of Positive Curvature [361] --
Problems [368] --
Appendix A: Review of Smooth Manifolds [371] --
Topological Preliminaries [371] --
Smooth Manifolds and Smooth Maps [374] --
Tangent Vectors [376] --
Submanifolds [378] --
Vector Bundles [382] --
The Tangent Bundle and Vector Fields [384] --
Smooth Covering Maps [388] --
Appendix B: Review of Tensors [391] --
Tensors on a Vector Space [391] --
Tensor Bundles and Tensor Fields [396] --
Differential Forms and Integration [400] --
Densities [405] --
Appendix C: Review of Lie Groups [407] --
Definitions and Properties [407] --
The Lie Algebra of a Lie Group [408] --
Group Actions on Manifolds [411] --
References [415] --
Notation Index [419] --
Subject Index [423] --

MR, MR3887684

There are no comments for this item.

Log in to your account to post a comment.

Click on an image to view it in the image viewer

¿Necesita ayuda?

Si necesita ayuda para encontrar información, puede visitar personalmente la biblioteca en Av. Alem 1253 Bahía Blanca, llamarnos por teléfono al 291 459 5116, o enviarnos un mensaje a bibima@criba.edu.ar.
Para solicitar copias de artículos, complete el formulario o escríbanos a pedidos.inmabb@gmail.com

Powered by Koha