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Zusatztext This book is an introductory graduate-level textbook on the theory of smoothmanifolds, for students who already have a solid acquaintance with generaltopology, the fundamental group, and covering spaces, as well as basicundergraduate linear algebra and real analysis. It is a natural sequelto the author's last book, Introduction to Topological Manifolds(2000).While the subject is often called "differential geometry," in this bookthe author has decided to avoid use of this term because it applies morespecifically to the study of smooth manifolds endowed with some extra structure,such as a Riemannian metric, a symplectic structure, a Lie group structure,or a foliation, and of the properties that are invariant under maps thatpreserve the structure. Although this text addresses these subjects, theyare treated more as interesting examples to which to apply the generaltheory than as objects of study in their own right. A student who finishesthis book should be well prepared to go on to study any of these specializedsubjects in much greater depth. Klappentext Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why Inhaltsverzeichnis Preface * Smooth Manifolds * Smooth Maps * Tangent Vectors * Vector Fields * Vector Bundles * The Cotangent Bundle * Submersions, Immersions, and Embeddings * Submanifolds * Lie Groups Actions * Embedding and Approximation Theorems * Tensors * Differential Forms * Orientations * Integration on Manifolds * De Rham Cohomology * The de Rham Theorem * Integral Curves and Flows * Lie Derivatives * Integral Manifolds and Foliations * Lie Groups and Their Lie Algebras * Appendix: Review of Prerequisites * References * Index ...
