Smooth Manifolds

Rajnikant Sinha (Autor)

Buch | Hardcover

485 Seiten

2014
Springer, India, Private Ltd (Verlag)
978-81-322-2103-6 (ISBN)

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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.

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.

Chapter 1. Differentiable Manifolds.- Chapter 2. Tangent Spaces.- Chapter 3. Multivariable Differential Calculus.- Chapter 4. Topological Properties of Smooth Manifolds.- Chapter 5. Immersions, Submersions, and Embeddings.- Chapter 6. Sard’s Theorem.- Chapter 7. Whitney Embedding Theorem.- Bibliography.

Zusatzinfo	10 Illustrations, black and white; IX, 485 p. 10 illus.
Verlagsort	New Delhi
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	differential manifolds • Multivariable differential calculus • Sard’s theorem • Smooth manifolds • Tangent bundles • Whitney’s theorem
ISBN-10	81-322-2103-6 / 8132221036
ISBN-13	978-81-322-2103-6 / 9788132221036
Zustand	Neuware