截面曲率 meaning in Chinese
sectional curvature
Examples
- 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则曲线及二、三、四维空间中的仿射星形曲线。 - The maximum designed compression ratio of two types of special - shaped columns is presented with two methods of curvature ductility and big - small eccentricity failure . and the advantages and disadvantages of the designed compression ratio determined by the two methods is compared to
用截面曲率延性和大小偏心临界破坏点两种方法确定它们的轴压比限值，并比较了两种方法确定轴压比限值的优缺点。 - As a result , ( i ) let k ( x ) be the function assign to each point x of m the infinimum of the sectional curvatures of m at that ponit , if k ( x ) satisfies , then m is totally umbilical . ( ii ) let q ( x ) be the function assign to each point x of m the infinimum of the ricci curvatures of m at that ponit , if q ( x ) satisfies q > 1 / 4 ( n - 2 ) ( c + 4h2 ) - 1 / 4nc , then m is totally umbilical , ( iii ) let a be the square length of the second fundermental form , if satisfies , then m is totally umbilical
) )中具有非零平行法平均曲率向量的紧致全实伪脐子流形m ~ n ，得到了( ? )如果m ~ n在其点x的截面曲率的下确界函数k ( x )满足条件：则m ~ n是全脐的( ? )如果m ~ n在其点x的ricci曲率的下确界函数q ( x )满足条件：则m ~ n是全脐的。 ( ? )如果m在m中的第二基本形式h长度的平方满足条件：则m ~ n是全脐的。 - 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。