Differential Geometry

Basic Notions and Physical Examples

  • Marcelo¬†Epstein

Part of the Mathematical Engineering book series (MATHENGIN)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Marcelo Epstein
    Pages 1-23
  3. Marcelo Epstein
    Pages 25-35
  4. Marcelo Epstein
    Pages 37-111
  5. Marcelo Epstein
    Pages 113-135
  6. Back Matter
    Pages 137-139

About this book


Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics.

Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constitutive response of continuous media.

Once these ideas have been grasped at the topological level, the differential structure needed for the description of physical fields is introduced in terms of differentiable manifolds and principal frame bundles. These mathematical concepts are then illustrated with examples from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy fluxes and dislocation theory.

This book will be useful for researchers and graduate students in science and engineering.


Continuum Mechanics Differential Forms Dislocations Fibre Bundles Groupoids Lie Groups Parallel Transport Topological and Differentiable Manifolds de Rham Currents

Authors and affiliations

  • Marcelo¬†Epstein
    • 1
  1. 1.Department of Mechanical and Manufacturing EngineeringUniversity of CalgaryCalgaryCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-06920-3
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-06919-7
  • Online ISBN 978-3-319-06920-3
  • Series Print ISSN 2192-4732
  • Series Online ISSN 2192-4740
  • About this book