English Dictionary

holonomy

名詞

(differential geometry) Given a smooth closed curve C on a surface M, and picking any point P on that curve, the holonomy of C in M is the angle by which some vector turns as it is parallel transported along the curve C from point P all the way around and back to point P.

日本語の意味

ホロノミー：微分幾何学における概念で、滑らかな閉曲線上の任意の一点から出発し、その曲線に沿って並行移動させたベクトルが、元の地点に戻る際に回転する角度を示すもの。

To determine the holonomy of a closed curve C on a smooth surface M, parallel-transport a tangent vector from a point P all the way around C back to P and measure the angle by which it has rotated.

滑らかな曲面 M 上の閉曲線 C の平行移動によって生じる角度を求めるには、点 P から接ベクトルを曲線 C に沿って一周させて P に戻し、その回転角を測定する。

意味（1）

(differential geometry) Given a smooth closed curve C on a surface M, and picking any point P on that curve, the holonomy of C in M is the angle by which some vector turns as it is parallel transported along the curve C from point P all the way around and back to point P.

holonomies （ plural ）