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 


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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

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