Differentiable manifolds: a first course Birkhäuser Advanced Texts
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Von Händler/Antiquariat, Petra Gros [1048006], Koblenz, Germany.
395 S. Das hier angebotene Buch stammt aus einer teilaufgelösten wissenschaftlichen Bibliothek und trägt die entsprechenden Kennzeichnungen (Rückenschild, Instituts-Stempel.). BDer Buchzustand ist ansonsten ordentlich und dem Alter entsprechend gut. TABLE OF CONTENTS Preface xi Acknowledgments xiii Chapter 1. Topological Manifolds 1 1.1. Locally Euclidean Spaces 1 1.2. Manifolds 3 1.3. Quotient Constructions and 2-Manifolds 7 1.4. Partitions of Unity 15 1.5. Imbeddings and Immersions 18 1.6. Manifolds with Boundary 20 Chapter 2. Local Theory 25 2.1. Differentiability Classes 25 2.2. Tangent Vectors 27 2.3. Smooth Maps and Their Differentials 34 2.4. Diffeomorphisms and Maps of Constant Rank 38 2.5. Smooth Submanifolds of Euclidean Space 42 2.6. Constructions of Smooth Functions 47 2.7. Smooth Vector Fields 50 2.8. Local Flows 55 2.9. Critical Points and Critical Values 64 Chapter 3. Global Theory 67 3.1. Smooth Manifolds and Mappings 67 3.2. Diffeomorphic Structures 73 3.3. The Tangent Bündle 74 3.4. Cocycles and Geometrie Structures 78 vüi CONTENTS 3.5. Global Constructions of Smooth Functions 84 3.6. Manifolds with Boundary 87 3.7. Submanifolds 91 3.8. Homotopy and Isotopy 93 3.9. Degree Theory 95 Chapter 4. Flows and Foliation 101 4.1. Complete Vector Fields 101 4.2. The Lie Bracket 107 4.3. Commuting Flows 110 4.4. Foliations 116 Chapter 5. Lie Groups 127 5.1. Basic Dennitions and Facts 127 5.2. Lie Subgroups and Subalgebras 136 5.3. Closed Subgroups 139 5.4. Homogeneous Spaces 145 5.5. Principal Bundles 150 Chapter 6. Covectors and 1—Forms 159 6.1. The Space of 1-Forms 159 6.2. Line Integrals 167 6.3. The First Cohomology Space 173 6.4. Some Topological Applications 180 Chapter 7. Multilinear Algebra 189 7.1. Tensor Algebra 189 7.2. Exterior Algebra 199 7.3. Symmetrie Algebra 207 7.4. Multilinear Bündle Theory 209 7.5. The Module of Sections 212 CONTENTS ix Chapter 8. Integration and Cohomology 221 8.1. The Exterior Derivative 221 8.2. Stokes' Theorem and Singular Homology 228 8.3. The Poincare Lemma 243 8.4. Exact Sequences 249 8.5. Mayer-Vietoris Sequences 252 8.6. Computations of Cohomology 257 8.7. Degree Theory . . 260 8.8. Poincare Duality 263 8.9. The de Rham Theorem 268 Chapter 9. Forms and Foliations 277 9.1. The Frobenius Theorem Revisited 277 9.2. The Normal Bündle and Transversality 281 9.3. Closed, Nonsingular 1-Forms 286 Chapter 10. Riemannian Geometry 293 10.1. Connections 294 10.2. Riemannian Manifolds 302 10.3. Gauss Curvature 306 10.4. Complete Riemannian Manifolds 314 10.5. Geodesic Convexity 327 10.6. The Cartan Structure Equations 331 10.7. Riemannian Homogeneous Spaces 344 Appendix A. Vector Fields on Spheres 349 Appendix B. Inverse Function Theorem 353 Appendix C. Ordinary Differential Equations 359 C.l. Existence and uniqueness of Solutions 360 C.2. A digression concerning Banach Spaces 362 l x CONTENTS C.3. Smooth dependence on initial conditions 364 C.4. The Linear Case 366 Appendix D. Sard's Theorem 367 Appendix E. de Rham—Cech Theorem 371 E.l. Cech cohomology 371 > E.2. The de Rham-Cech complex 375 Bibliography 383 Index 385 Sprache: Englisch Gewicht in Gramm: 810.

Von Händler/Antiquariat, Petra Gros [1048006], Koblenz, Germany.
395 S. Das hier angebotene Buch stammt aus einer teilaufgelösten wissenschaftlichen Bibliothek und trägt die entsprechenden Kennzeichnungen (Rückenschild, Instituts-Stempel.). BDer Buchzustand ist ansonsten ordentlich und dem Alter entsprechend gut. TABLE OF CONTENTS Preface xi Acknowledgments xiii Chapter 1. Topological Manifolds 1 1.1. Locally Euclidean Spaces 1 1.2. Manifolds 3 1.3. Quotient Constructions and 2-Manifolds 7 1.4. Partitions of Unity 15 1.5. Imbeddings and Immersions 18 1.6. Manifolds with Boundary 20 Chapter 2. Local Theory 25 2.1. Differentiability Classes 25 2.2. Tangent Vectors 27 2.3. Smooth Maps and Their Differentials 34 2.4. Diffeomorphisms and Maps of Constant Rank 38 2.5. Smooth Submanifolds of Euclidean Space 42 2.6. Constructions of Smooth Functions 47 2.7. Smooth Vector Fields 50 2.8. Local Flows 55 2.9. Critical Points and Critical Values 64 Chapter 3. Global Theory 67 3.1. Smooth Manifolds and Mappings 67 3.2. Diffeomorphic Structures 73 3.3. The Tangent Bündle 74 3.4. Cocycles and Geometrie Structures 78 vüi CONTENTS 3.5. Global Constructions of Smooth Functions 84 3.6. Manifolds with Boundary 87 3.7. Submanifolds 91 3.8. Homotopy and Isotopy 93 3.9. Degree Theory 95 Chapter 4. Flows and Foliation 101 4.1. Complete Vector Fields 101 4.2. The Lie Bracket 107 4.3. Commuting Flows 110 4.4. Foliations 116 Chapter 5. Lie Groups 127 5.1. Basic Dennitions and Facts 127 5.2. Lie Subgroups and Subalgebras 136 5.3. Closed Subgroups 139 5.4. Homogeneous Spaces 145 5.5. Principal Bundles 150 Chapter 6. Covectors and 1—Forms 159 6.1. The Space of 1-Forms 159 6.2. Line Integrals 167 6.3. The First Cohomology Space 173 6.4. Some Topological Applications 180 Chapter 7. Multilinear Algebra 189 7.1. Tensor Algebra 189 7.2. Exterior Algebra 199 7.3. Symmetrie Algebra 207 7.4. Multilinear Bündle Theory 209 7.5. The Module of Sections 212 CONTENTS ix Chapter 8. Integration and Cohomology 221 8.1. The Exterior Derivative 221 8.2. Stokes' Theorem and Singular Homology 228 8.3. The Poincare Lemma 243 8.4. Exact Sequences 249 8.5. Mayer-Vietoris Sequences 252 8.6. Computations of Cohomology 257 8.7. Degree Theory . . 260 8.8. Poincare Duality 263 8.9. The de Rham Theorem 268 Chapter 9. Forms and Foliations 277 9.1. The Frobenius Theorem Revisited 277 9.2. The Normal Bündle and Transversality 281 9.3. Closed, Nonsingular 1-Forms 286 Chapter 10. Riemannian Geometry 293 10.1. Connections 294 10.2. Riemannian Manifolds 302 10.3. Gauss Curvature 306 10.4. Complete Riemannian Manifolds 314 10.5. Geodesic Convexity 327 10.6. The Cartan Structure Equations 331 10.7. Riemannian Homogeneous Spaces 344 Appendix A. Vector Fields on Spheres 349 Appendix B. Inverse Function Theorem 353 Appendix C. Ordinary Differential Equations 359 C.l. Existence and uniqueness of Solutions 360 C.2. A digression concerning Banach Spaces 362 l x CONTENTS C.3. Smooth dependence on initial conditions 364 C.4. The Linear Case 366 Appendix D. Sard's Theorem 367 Appendix E. de Rham—Cech Theorem 371 E.l. Cech cohomology 371 > E.2. The de Rham-Cech complex 375 Bibliography 383 Index 385 Sprache: Englisch Gewicht in Gramm: 810, Books.

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Von Händler/Antiquariat, Petra Gros, [3076014].
395 S. gebundene Ausgabe Das hier angebotene Buch stammt aus einer teilaufgelösten wissenschaftlichen Bibliothek und trägt die entsprechenden Kennzeichnungen (Rückenschild, Instituts-Stempel...). BDer Buchzustand ist ansonsten ordentlich und dem Alter entsprechend gut. TABLE OF CONTENTS Preface xi Acknowledgments xiii Chapter 1. Topological Manifolds 1 1.1. Locally Euclidean Spaces 1 1.2. Manifolds 3 1.3. Quotient Constructions and 2-Manifolds 7 1.4. Partitions of Unity 15 1.5. Imbeddings and Immersions 18 1.6. Manifolds with Boundary 20 Chapter 2. Local Theory 25 2.1. Differentiability Classes 25 2.2. Tangent Vectors 27 2.3. Smooth Maps and Their Differentials 34 2.4. Diffeomorphisms and Maps of Constant Rank 38 2.5. Smooth Submanifolds of Euclidean Space 42 2.6. Constructions of Smooth Functions 47 2.7. Smooth Vector Fields 50 2.8. Local Flows 55 2.9. Critical Points and Critical Values 64 Chapter 3. Global Theory 67 3.1. Smooth Manifolds and Mappings 67 3.2. Diffeomorphic Structures 73 3.3. The Tangent Bündle 74 3.4. Cocycles and Geometrie Structures 78 vüi CONTENTS 3.5. Global Constructions of Smooth Functions 84 3.6. Manifolds with Boundary 87 3.7. Submanifolds 91 3.8. Homotopy and Isotopy 93 3.9. Degree Theory 95 Chapter 4. Flows and Foliation 101 4.1. Complete Vector Fields 101 4.2. The Lie Bracket 107 4.3. Commuting Flows 110 4.4. Foliations 116 Chapter 5. Lie Groups 127 5.1. Basic Dennitions and Facts 127 5.2. Lie Subgroups and Subalgebras 136 5.3. Closed Subgroups 139 5.4. Homogeneous Spaces 145 5.5. Principal Bundles 150 Chapter 6. Covectors and 1Forms 159 6.1. The Space of 1-Forms 159 6.2. Line Integrals 167 6.3. The First Cohomology Space 173 6.4. Some Topological Applications 180 Chapter 7. Multilinear Algebra 189 7.1. Tensor Algebra 189 7.2. Exterior Algebra 199 7.3. Symmetrie Algebra 207 7.4. Multilinear Bündle Theory 209 7.5. The Module of Sections 212 CONTENTS ix Chapter 8. Integration and Cohomology 221 8.1. The Exterior Derivative 221 8.2. Stokes' Theorem and Singular Homology 228 8.3. The Poincare Lemma 243 8.4. Exact Sequences 249 8.5. Mayer-Vietoris Sequences 252 8.6. Computations of Cohomology 257 8.7. Degree Theory . . 260 8.8. Poincare Duality 263 8.9. The de Rham Theorem 268 Chapter 9. Forms and Foliations 277 9.1. The Frobenius Theorem Revisited 277 9.2. The Normal Bündle and Transversality 281 9.3. Closed, Nonsingular 1-Forms 286 Chapter 10. Riemannian Geometry 293 10.1. Connections 294 10.2. Riemannian Manifolds 302 10.3. Gauss Curvature 306 10.4. Complete Riemannian Manifolds 314 10.5. Geodesic Convexity 327 10.6. The Cartan Structure Equations 331 10.7. Riemannian Homogeneous Spaces 344 Appendix A. Vector Fields on Spheres 349 Appendix B. Inverse Function Theorem 353 Appendix C. Ordinary Differential Equations 359 C.l. Existence and uniqueness of Solutions 360 C.2. A digression concerning Banach Spaces 362 l x CONTENTS C.3. Smooth dependence on initial conditions 364 C.4. The Linear Case 366 Appendix D. Sard's Theorem 367 Appendix E. de RhamCech Theorem 371 E.l. Cech cohomology 371 E.2. The de Rham-Cech complex 375 Bibliography 383 Index 385, gebraucht gut, 810g.

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Differentiable-Manifolds~~Lawrence-Conlon, Differentiable Manifolds: A First Course.