English Dictionary

differentiable manifold

名詞

(differential geometry) A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;

日本語の意味

微分可能多様体：局所的にはユークリッド空間に十分類似しており、微分積分学を適用できる多様体

When studying the curvature of a differentiable manifold, one often relies on coordinate charts to perform calculations.

微分可能多様体の曲率を研究する際には、計算を行うために座標図に頼ることが多い。

意味（1）

(differential geometry) A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;

The charts (homeomorphisms) that make up any differentiable structure of a differentiable manifold are required to be such that the transition from one to another is differentiable.

意味（2）

(more formally) a manifold that can be equipped with a differentiable structure (an atlas of ℝⁿ-compatible charts).

differentiable manifolds （ plural ）