contact geometry

countable uncountable

(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;

Japanese Meaning

接触幾何学：滑らかな奇数次元多様体上で、接触分布（あるいは接触構造）と呼ばれる、完全非可積分性を示す（局所的には最大非退化な微分1形式の核として定義される）接触構造を研究する微分幾何学の一分野。

What is this buttons?

Contact geometry studies maximally nondegenerate hyperplane distributions on odd-dimensional smooth manifolds and their associated Reeb dynamics.

Google Translation / DeepL Translation

接触幾何学は、奇数次元の滑らかな多様体上で最大限に非退化した1形式の核として表される完全に非積分可能な接平面分布と、それに伴うリーブ流の力学を研究する中心的な微分幾何学の分野です。

Details

Sense（1）

The defining conditions for a contact geometry are opposite to two equivalent conditions for complete integrability of a hyperplane distribution: i.e. that it be tangent to a codimension 1 foliation on the manifold, whose equivalence is the content of the Frobenius theorem.

Google Translation / DeepL Translation