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- catalog abstract "This book is an introductory graduate-level textbook on the theory of smooth manifolds, for students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. It is a natural sequel to the author's last book, Introduction to Topological Manifolds(2000). While the subject is often called "differential geometry," in this book the author has decided to avoid use of this term because it applies more specifically 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 that preserve the structure. Although this text addresses these subjects, they are treated more as interesting examples to which to apply the general theory than as objects of study in their own right. A student who finishes this book should be well prepared to go on to study any of these specialized subjects in much greater depth.".
- catalog contributor b12598794.
- catalog created "c2003.".
- catalog date "2003".
- catalog date "c2003.".
- catalog dateCopyrighted "c2003.".
- catalog description "Includes bibliographical references (p. [597]-599) and index.".
- catalog description "Preface -- Smooth Manifolds -- Smooth Maps -- Tangent Vectors -- Vector Fields -- Vector Bundles -- The Cotangent Bundle -- Submersions, Immersions, and Embeddings -- Submanifolds -- Embedding and Approximation Theorems -- Lie Group Actions -- 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.".
- catalog description "This book is an introductory graduate-level textbook on the theory of smooth manifolds, for students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. It is a natural sequel to the author's last book, Introduction to Topological Manifolds(2000). While the subject is often called "differential geometry," in this book the author has decided to avoid use of this term because it applies more specifically 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 that preserve the structure. Although this text addresses these subjects, they are treated more as interesting examples to which to apply the general theory than as objects of study in their own right. A student who finishes this book should be well prepared to go on to study any of these specialized subjects in much greater depth.".
- catalog extent "xvii, 629 p. :".
- catalog identifier "0387954481 (pbk. : alk. paper)".
- catalog identifier "0387954953 (alk. paper)".
- catalog isPartOf "Graduate texts in mathematics ; 218".
- catalog issued "2003".
- catalog issued "c2003.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "514/.3 21".
- catalog subject "Cell aggregation Mathematics.".
- catalog subject "Global differential geometry.".
- catalog subject "Manifolds (Mathematics)".
- catalog subject "Mathematics.".
- catalog subject "QA613 .L44 2003".
- catalog tableOfContents "Preface -- Smooth Manifolds -- Smooth Maps -- Tangent Vectors -- Vector Fields -- Vector Bundles -- The Cotangent Bundle -- Submersions, Immersions, and Embeddings -- Submanifolds -- Embedding and Approximation Theorems -- Lie Group Actions -- 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.".
- catalog title "Introduction to smooth manifolds / John M. Lee.".
- catalog type "text".