TY -
GEN
AU - Lee, John M.
TI -
Introduction to Smooth Manifolds
ET - 2nd ed. 2012
PB - Springer
SN - 9781441999825
KW - Global differential geometry
KW - Mathematics
KW - Differential geometry.
KW - Manifolds (Mathematics)
KW - Glatte Mannigfaltigkeit
KW - Glatte Kurve
KW - Glatte Fläche
PY - 2012
N2 - Description based upon print version of record
N2 - Introduction to Smooth Manifolds; Preface; Prerequisites; Exercises and Problems; About the Second Edition; Acknowledgments; Contents; Chapter 1: Smooth Manifolds; Topological Manifolds; Coordinate Charts; Examples of Topological Manifolds; Topological Properties of Manifolds; Connectivity; Local Compactness and Paracompactness; Fundamental Groups of Manifolds; Smooth Structures; Local Coordinate Representations; Examples of Smooth Manifolds; The Einstein Summation Convention; More Examples; Manifolds with Boundary; Smooth Structures on Manifolds with Boundary; Problems
N2 - Chapter 2: Smooth MapsSmooth Functions and Smooth Maps; Smooth Functions on Manifolds; Smooth Maps Between Manifolds; Diffeomorphisms; Partitions of Unity; Applications of Partitions of Unity; Problems; Chapter 3: Tangent Vectors; Tangent Vectors; Geometric Tangent Vectors; Tangent Vectors on Manifolds; The Differential of a Smooth Map; Computations in Coordinates; The Differential in Coordinates; Change of Coordinates; The Tangent Bundle; Velocity Vectors of Curves; Alternative Definitions of the Tangent Space; Tangent Vectors as Derivations of the Space of Germs
N2 - Tangent Vectors as Equivalence Classes of CurvesTangent Vectors as Equivalence Classes of n-Tuples; Categories and Functors; Problems; Chapter 4: Submersions, Immersions, and Embeddings; Maps of Constant Rank; Local Diffeomorphisms; The Rank Theorem; The Rank Theorem for Manifolds with Boundary; Embeddings; Submersions; Smooth Covering Maps; Problems; Chapter 5: Submanifolds; Embedded Submanifolds; Slice Charts for Embedded Submanifolds; Level Sets; Immersed Submanifolds; Restricting Maps to Submanifolds; Uniqueness of Smooth Structures on Submanifolds; Extending Functions from Submanifolds
N2 - The Tangent Space to a SubmanifoldSubmanifolds with Boundary; Problems; Chapter 6: Sard's Theorem; Sets of Measure Zero; Sard's Theorem; The Whitney Embedding Theorem; The Whitney Approximation Theorems; Tubular Neighborhoods; Smooth Approximation of Maps Between Manifolds; Transversality; Problems; Chapter 7: Lie Groups; Basic Definitions; Lie Group Homomorphisms; The Universal Covering Group; Lie Subgroups; Group Actions and Equivariant Maps; Equivariant Maps; Semidirect Products; Representations; Problems; Chapter 8: Vector Fields; Vector Fields on Manifolds; Local and Global Frames
N2 - Vector Fields as Derivations of Cinfty(M)Vector Fields and Smooth Maps; Vector Fields and Submanifolds; Lie Brackets; The Lie Algebra of a Lie Group; Induced Lie Algebra Homomorphisms; The Lie Algebra of a Lie Subgroup; Problems; Chapter 9: Integral Curves and Flows; Integral Curves; Flows; The Fundamental Theorem on Flows; Complete Vector Fields; Flowouts; Regular Points and Singular Points; Flows and Flowouts on Manifolds with Boundary; Lie Derivatives; Commuting Vector Fields; Commuting Frames; Time-Dependent Vector Fields; First-Order Partial Differential Equations; Linear Equations
N2 - Quasilinear Equations
BT - Graduate Texts in Mathematics ; 218
BT - SpringerLink ; Bücher
CY - New York, NY [u.a.]
UR - http://slubdd.de/katalog?TN_libero_mab2
ER -