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Transverse Geometry

  • Pierre Molino
Part of the Progress in Mathematics book series (PM, volume 73)

Abstract

If F is a simple foliation defined on the manifold M by the projection π: M ➞ W onto a quotient manifold, then the “transverse geometry” is precisely the differential geometry of the quotient manifold. In general, in the case of an arbitrary foliation, there no longer exists a global quotient manifold. Nevertheless, the condition for a geometric structure to be “locally projectable along the leaves” still has a precise meaning. The study of structures that possess this property constitutes the transverse geometry of the foliation. These ideas have their origin in the works of C.Ehresmann [Eh] and A.Haefliger [Ha]2.

Keywords

Principal Bundle Transverse Field Riemannian Foliation Simple Foliation Projectable Connection 
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.

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Copyright information

© Birkhäuser Boston 1988

Authors and Affiliations

  • Pierre Molino
    • 1
  1. 1.Institut de MathématiquesUniversité des Sciences et Techniques du LanguedocMontpellier CedexFrance

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