gauss curvature 中文意思是什麼
gauss curvature
解釋
高斯曲率-
On the other hand, the conformal deformation ' s problem is to find a metric on h2 ( - 1 ), conformal to g, with the given function k as its gaussian curvature, that is, it is important for us to study the solvability of the conformal gauss curvature equation in geometry analysis. the problem that the conformal gauss curvature equation may have a solution for every nonegative holder continuous function k ( x ) is also an open problem
） = e ~ （ 2u ） g使k是（ ? ）的高斯曲率，即共形高斯曲率方程的可解性研究是幾何分析中的一個重要問題。當預定的函數k取正值時，共形高斯曲率方程解的存在性命題作為一個猜測至今未得到解決。 -
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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