Overview
- Presents detailed proofs of important theorems
- Supplies solved examples for each concept discussed
- Discusses all major topics on smooth manifolds
- Proves Sard’s theorem, for the first time, in case n = 1
- Will be useful for graduate students as well as researchers
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Table of contents (7 chapters)
Keywords
About this book
This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry. The book primarily focuses on topics concerning differential manifolds, tangent spaces, multivariable differential calculus, topological properties of smooth manifolds, embedded submanifolds, Sard’s theorem and Whitney embedding theorem. It is clearly structured, amply illustrated and includes solved examples for all concepts discussed. Several difficult theorems have been broken into many lemmas and notes (equivalent to sub-lemmas) to enhance the readability of the book. Further, once a concept has been introduced, it reoccurs throughout the book to ensure comprehension. Rank theorem, a vital aspect of smooth manifolds theory, occurs in many manifestations, including rank theorem for Euclidean space and global rank theorem. Though primarily intended for graduate studentsof mathematics, the book will also prove useful for researchers. The prerequisites for this text have intentionally been kept to a minimum so that undergraduate students can also benefit from it. It is a cherished conviction that “mathematical proofs are the core of all mathematical joy,” a standpoint this book vividly reflects.
Authors and Affiliations
About the author
Rajnikant Sinha is former professor of mathematics at Magadh University, Bodh Gaya, India. A passionate mathematician by heart, Prof. Sinha has published several interesting researches in international journals and contributed a book Solutions to Weatherburn’s Elementary Vector Analysis. His research areas are topological vector spaces, differential geometry and manifolds.
Bibliographic Information
Book Title: Smooth Manifolds
Authors: Rajnikant Sinha
DOI: https://doi.org/10.1007/978-81-322-2104-3
Publisher: Springer New Delhi
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer India 2014
Hardcover ISBN: 978-81-322-2103-6Published: 01 December 2014
Softcover ISBN: 978-81-322-2955-1Published: 22 September 2016
eBook ISBN: 978-81-322-2104-3Published: 15 November 2014
Edition Number: 1
Number of Pages: IX, 485
Number of Illustrations: 10 b/w illustrations
Topics: Differential Geometry, Classical and Quantum Gravitation, Relativity Theory, Global Analysis and Analysis on Manifolds