.

0 (hodnocen0 x )

BK

1st ed.

Singapore : World Scientific, 2000

x,356 s.

ISBN 981-02-3494-5 (váz.)

Series on university mathematics ; [vol.] 1

Obsahuje bibliografii na s. 343-346 a rejstřík

Geometrie diferenciální - učebnice vysokošk.

000052090

1 Differentiable Manifolds 1 // §1-1 Definition of Differentiable Manifolds... 1 // §1-2 Tangent Spaces...-... 9 // §1-3 Submanifolds... 18 // §1-4 Frobenius’ Theorem... 29 // 2 Multilinear Algebra 39 // §2-1 Tensor Products ... 39 // §2-2 Tensors... 47 // §2-3 Exterior Algebra... 52 // 3 Exterior Differential Calculus 65 // §3-1 Tensor Bundles and Vector Bundles ... 65 // §3-2 Exterior Differentiation ... 74 // §3-3 Integrals of Differential Forms... 85 // §3-4 Stokes’ Formula... 92 // 4 Connections 101 // §4-1 Connections on Vector Bundles...101 // §4-2 Affine Connections...113 // §4-3 Connections on Frame Bundles...121 // 5 Riemannian Geometry 133 // §5-1 The Fundamental Theorem of Riemannian Geometry...133 // §5-2 Geodesic Normal Coordinates...143 // §5-3 Sectional Curvature ...155 // §5-4 The Gauss-Bonnet Theorem ...162 // 6 Lie Groups and Moving Frames 173 // §6-1 Lie Groups ...173 // §6-2 Lie Transformation Groups...186 // §6-3 The Method of Moving Frames...198 // X CONTENTS // §6-4 Theory of Surfaces...210 // 7 Complex Manifolds 221 // §7-1 Complex Manifolds...221 // §7-2 The Complex Structure on a Vector Space...227 // §7-3 Almost Complex Manifolds...236 // §7-4 Connections on Complex Vector Bundles...244 // §7-5 Hermitian Manifolds and Kählerian Manifolds...256 // 8 Finsler Geometry 265 // §8-1 Preliminaries...265 // §8-2 Geometry on the Projectivised Tangent Bundle (PTM) and the // Hilbert Form...267 // §8-3 The Chern Connection...273

// §8-3.1 Determination of the Connection...274 // §8-3.2 The Cartan Tensor and Characterization of Riemannian // Geometry...280 // §8-3.3 Explicit Formulas for the Connection Forms in Natural // Coordinates...283 // §8-4 Structure Equations and the Flag Curvature...288 // §8-4.1 The Curvature Tensor...289 // §8-4.2 The Flag Curvature and the Ricci Curvature...293 // §8-4.3 Special Finsler Spaces...295 // §8-5 The First Variation of Arc Length and Geodesics...297 // §8-6 The Second Variation of Arc Length and Jacobi Fields...306 // §8-7 Completeness and the Hopf-Rinow Theorem...314 // §8-8 The Theorems of Bonnet-Myers and Synge ...325 // A Historical Notes 331 // § ?-l Classical Differential Geometry...331 // §A-2 Riemannian Geometry...331 // §A-3 Manifolds...332 // §A-4 Global Geometry...332 // ? Differential Geometry and Theoretical Physics 335 // §B-1 Dynamics and Moving Frames...336 // §B-2 Theory of Surfaces, Solitons and the Sigma Model...338 // §B-3 Gauge Field Theory...340 // §B-4 Conclusion ...341 // References 343 // Index // 347