English Dictionary

contact geometry

名詞

可算名詞 不可算名詞

(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;

日本語の意味

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。

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

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。

意味（1）

(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;

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.

意味（2）

(uncountable) the study of such structures.

意味（3）

Used other than figuratively or idiomatically: see contact, geometry.

Surfaces of even the large hydrate particles have rounded protrusions and are best represented by a sphere-sphere contact geometry.

contact geometries （ plural ）