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Mathematics - Geometry & Topology | Differential Geometry - Basic Notions and Physical Examples

Differential Geometry

Basic Notions and Physical Examples

Epstein, Marcelo

2014, XI, 139 p. 26 illus.

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  • Provides a comprehensive description of the geometric constructs that form the backbone of modern differential geometry
  • Demonstrates the close correspondence between geometrical objects and physically meaningful counterparts in engineering and physics
  • Treatment is not overly technical from the mathematical point of view, thus allowing for a comfortable mastery of the essential ideas

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.

Content Level » Research

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

Related subjects » Classical Continuum Physics - Geometry & Topology - Mechanics - Theoretical, Mathematical & Computational Physics

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