Manifolds and Smooth Structures

  • Juan-Pablo Ortega
  • Tudor S. Ratiu
Part of the Progress in Mathematics book series (PM, volume 222)


The purpose of this chapter is to have a handy glossary of definitions, notation, con¬ventions, and theorems in elementary manifold theory. The reader should use it only as a source of information whenever the need arises. The style used in the exposition will be merely descriptive and the statements will be framed under the form of a result only when either a short proof is given because it is not readily available in the litera¬ture or when they will be needed for future reference. The results quoted here can be found, for example, in Abraham and Marsden (1978); Abraham, Marsden, and Ratiu (1988); Abraham and Robbin (1967); Bourbaki (1971); Brickell and Clark (1970); Pflaum (2001a); Kobayashi and Nomizu (1963); Kolář, Michor, and Slovák (1993); Libermann and Marle (1987); Spanier (1966); Tondeur (1997); Warner (1983).


Vector Field Vector Bundle Topological Space Open Neighborhood Smooth Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Juan Pablo Ortega and Tudor S. Ratiu 2004

Authors and Affiliations

  • Juan-Pablo Ortega
    • 1
  • Tudor S. Ratiu
    • 2
  1. 1.CNRS-Laboratoire de Mathématiques de BensançonUniversité de Franche-Comté, UFR des Sciences et TechniquesBensançon CedexFrance
  2. 2.Départment de MathématiquesLausanneSwitzerland

Personalised recommendations