正則星形線 的英文怎麼說
中文拼音 [zhēngzéxīngxíngxiàn]
正則星形線
英文
regular astroid- 正 : 正名詞(正月) the first month of the lunar year; the first moon
- 則 : Ⅰ名詞1 (規范) standard; norm; criterion 2 (規則) regulation; rule; law 3 (姓氏) a surname Ⅱ...
- 星 : 名詞1 (夜晚天空中閃爍發光的天體) star 2 [天文學] (宇宙間能發射光或反射光的天體) heavenly body...
- 線 : 名詞1 (用絲、棉、金屬等製成的細長的東西) thread; string; wire 2 [數學] (一個點任意移動所構成的...
- 正則 : holomorphic
- 星形 : star; starlike; stellate星形航空發動機 radial aeroengine; 星形空冷式發動機 radial air-cooled engine
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This paper deals with the regular curves in a riemannian manifold with constant sectional curvature and the affine starlike curves in r2, r3 and r4
本文研究了具有常截面曲率的黎曼流形中的正則曲線及二、三、四維空間中的仿射星形曲線。For the regular curves, we find two killing fields for the purpose of integrating the structural equations of the p - elastic curves and express the p - elastica by quadratures in a system of cylindrical coordinates. for the star - like affine curves, we solve the euler - lagrange equation by quadratures and reduced the higher order structure equation to a first order linear system by using killing field and the classification of linear lie algebra sl ( 2, r ), sl ( 3, r ) and sl ( 4, r ). we solve the centroaffine p - elastica completely by quadratures
對于正則曲線的情形,我們發現了兩個用於求解p -彈性曲線的結構方程的killing向量場並用積分將p -彈性曲線在一個柱面坐標系中表示出來,而對仿射星形曲線的情形,我們用積分方法解出了歐拉-拉格朗日方程,利用killing向量場及線性李代數s1 ( 2 , r ) 、 s1 ( 3 , r )和s1 ( 4 , r )的分類將高階結構方程降為一階線性方程,因此我們用積分完全解出了中心仿射p -彈性曲線。
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