gauss curvature造句

• 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几何分析中的一个重要问题。当预定的函数k取正值时，共形高斯曲率方程解的存在性命题作为一个猜测至今未得到解决。
• 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 )研究了实空间形式r ~ m ( c )中具有平行等参截面的紧致子流形m ，证明了具有一平行等参截面的子流形m ，如果m的截面曲率恒正，则m包含在r ~ m ( c )的一个超球面内；对于常曲率空间及r ~ 4 ( c )中具有常平均曲率的紧致曲面m ，如果m的高斯曲率处处大于零，则m或为r ~ m ( c )中的全测地曲面或为一球面。这里m上的等参截面是m上整体定义的单位法向量场，使得m关于它的平均曲率m _ 1 ( )是常数。