常曲率空间 meaning in Chinese
space of constant curvature space
Examples
- Some results on metric averaging in space with nonnegative constant curvature
关于非负常曲率空间中度量平均的几个结果 - On the hypersurfaces with constant mean curvature in a quasi constant curvature space
关于拟常曲率空间中具有常平均曲率超曲面 - In this paper , we studied the co - dimension decreasing of submanifold . we point out that on certain condition , the co - dime nsion can be reduced to 1
本文研究了常曲率空间子流形余维数减少的问题,说明了在一定条件下,余维数可以减少到1 - 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。