gauss constant 中文意思是什麼
gauss constant
解釋
高斯常數-
Theorem 1. 4 let m be a hypersurface with non - zero constant scalar curvature in rn + l spanning a sphere sn - 1 ( r ). if its gauss image lies in the semisphere, then m is a hypersphere cap
）為邊界的緊致常純量曲率（非零）超曲面，如果其高斯映照像落在一個以s ~ （ n - 1 ） （ r ）為邊界的半球面內，則m只有超球面蓋。 -
In the second part, we investigate the compact submanifolds m with the parallel isoperimetric section in the real space forms rm ( c ) and prove that if there exists a parallel isoperimetric section on m, and the sectional curvature of m is always greater than zero, then m is contained in a hyper - sphere ; and get that the gauss curvature of the compact surfaces m with constant mean curvature in constant curvature space r4 ( c ) is always greater than zero, then m is a totally geodesic surface or a sphere, where an isoperimetric on m means a unit normal vector field defined globally on m with m1 ( ) = constant
（ 2 ）研究了實空間形式r ~ m （ c ）中具有平行等參截面的緊致子流形m ，證明了具有一平行等參截面的子流形m ，如果m的截面曲率恆正，則m包含在r ~ m （ c ）的一個超球面內；對于常曲率空間及r ~ 4 （ c ）中具有常平均曲率的緊致曲面m ，如果m的高斯曲率處處大於零，則m或為r ~ m （ c ）中的全測地曲面或為一球面。這里m上的等參截面是m上整體定義的單位法向量場，使得m關於它的平均曲率m _ 1 （ ）是常數。
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