Analysis and Algebra on Differentiable Manifolds

A Workbook for Students and Teachers

  • Pedro M. Gadea
  • Jaime Muñoz Masqué
  • Ihor V. Mykytyuk

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages I-XXV
  2. Pedro M. Gadea, Jaime Muñoz Masqué, Ihor V. Mykytyuk
    Pages 1-87
  3. Pedro M. Gadea, Jaime Muñoz Masqué, Ihor V. Mykytyuk
    Pages 89-128
  4. Pedro M. Gadea, Jaime Muñoz Masqué, Ihor V. Mykytyuk
    Pages 129-148
  5. Pedro M. Gadea, Jaime Muñoz Masqué, Ihor V. Mykytyuk
    Pages 149-262
  6. Pedro M. Gadea, Jaime Muñoz Masqué, Ihor V. Mykytyuk
    Pages 263-342
  7. Pedro M. Gadea, Jaime Muñoz Masqué, Ihor V. Mykytyuk
    Pages 343-546
  8. Pedro M. Gadea, Jaime Muñoz Masqué, Ihor V. Mykytyuk
    Pages 547-600
  9. Back Matter
    Pages 601-617

About this book

Introduction

This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds.

The exercises go from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear.

A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics.

In this 2nd edition:
• 76 new problems
• a section devoted to a generalization of Gauss’ Lemma
• a short novel section dealing with some properties of the energy of Hopf vector fields
• an expanded collection of formulae and tables
• an extended bibliography

Audience

This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.

Keywords

Adjoint Representation Almost Complex Manifold Characteristic Classes Constant Curvature Differentiable Manifolds

Authors and affiliations

  • Pedro M. Gadea
    • 1
  • Jaime Muñoz Masqué
    • 2
  • Ihor V. Mykytyuk
    • 3
  1. 1.Instituto de Fisica FundamentalCSICMadridSpain
  2. 2.Instituto de SeguridadCSICMadridSpain
  3. 3.Institute of MathematicsPedagogical University of CracowCracowPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-007-5952-7
  • Copyright Information Springer-Verlag London 2013
  • Publisher Name Springer, Dordrecht
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-94-007-5951-0
  • Online ISBN 978-94-007-5952-7
  • Series Print ISSN 0941-3502
  • About this book
Industry Sectors
Aerospace
Oil, Gas & Geosciences