Contact Manifolds

  • David E. Blair
Part of the Progress in Mathematics book series (PM, volume 203)

Abstract

By a contact manifold we mean a C manifold M 2n+1 together with a 1-form η such that η ∧ () n ≠ 0. In particular η ∧ () n ≠ 0 is a volume element on M so that a contact manifold is orientable. Also has rank 2n on the Grassmann algebra ∧ T m * M at each point mM and thus we have a 1-dimensional subspace, {XT m M|(X, T m M) = 0}, on which η ≠ 0 and which is complementary to the subspace on which η = 0. Therefore choosing ξ m in this subspace normalized by η(ξ m ) = 1 we have a global vector field ξ satisfying
$$ d\eta \left( {\xi ,X} \right) = 0,\;\eta \left( \xi \right) = 1 $$
.

Keywords

Symplectic Manifold Contact Structure Contact Form Contact Manifold Coordinate Neighborhood 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • David E. Blair
    • 1
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

Personalised recommendations