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Differential Manifolds

  • Serge Lang

Table of contents

  1. Front Matter
    Pages i-ix
  2. Serge Lang
    Pages 1-19
  3. Serge Lang
    Pages 21-40
  4. Serge Lang
    Pages 41-60
  5. Serge Lang
    Pages 135-149
  6. Serge Lang
    Pages 151-169
  7. Serge Lang
    Pages 171-189
  8. Serge Lang
    Pages 191-213
  9. Back Matter
    Pages 215-230

About this book

Introduction

The present volume supersedes my Introduction to Differentiable Manifolds written a few years back. I have expanded the book considerably, including things like the Lie derivative, and especially the basic integration theory of differential forms, with Stokes' theorem and its various special formulations in different contexts. The foreword which I wrote in the earlier book is still quite valid and needs only slight extension here. Between advanced calculus and the three great differential theories (differential topology, differential geometry, ordinary differential equations), there lies a no-man's-land for which there exists no systematic exposition in the literature. It is the purpose of this book to fill the gap. The three differential theories are by no means independent of each other, but proceed according to their own flavor. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.). One may also use differentiable structures on topological manifolds to determine the topological structure of the manifold (e.g. it la Smale [26]).

Keywords

Immersion Submersion Tensor Volume differential geometry differential topology differenzierbare Mannigfaltigkeit exterior derivative manifold

Authors and affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information