Usually means: Mathematical study of infinitesimal symmetries.
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We found 3 dictionaries that define the word contact geometry:

General (2 matching dictionaries)
  1. Contact geometry: Wikipedia, the Free Encyclopedia
  2. contact geometry: Wiktionary

Computing (1 matching dictionary)
  1. Contact geometry: Encyclopedia

Definitions from Wiktionary (contact geometry)

noun:  (differential geometry, countable) Given a smooth manifold of odd dimensionality, a distribution (subset) of the tangent bundle that satisfies the condition of complete nonintegrability, or equivalently may be locally defined as the kernel of a maximally nondegenerate differential 1-form;
noun:  Used other than figuratively or idiomatically: see contact, geometry.

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