Smooth Manifolds / by Rajnikant Sinha.

Format:

Book

Author/Creator:

Sinha, Rajnikant, Author.

Language:

English

Subjects (All):

Geometry, Differential.

Gravitation.

Global analysis (Mathematics).

Manifolds (Mathematics).

Differential Geometry.

Classical and Quantum Gravitation, Relativity Theory.

Global Analysis and Analysis on Manifolds.

Local Subjects:

Differential Geometry.

Classical and Quantum Gravitation, Relativity Theory.

Global Analysis and Analysis on Manifolds.

Physical Description:

1 online resource (IX, 485 p. 10 illus.)

Edition:

1st ed. 2014.

Place of Publication:

New Delhi : Springer India : Imprint: Springer, 2014.

Language Note:

English

Summary:

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 students of 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.

Contents:

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

ISBN:

81-322-2104-4