sectional curvature meaning in English
截面曲率
Examples
- The holomorphic sectional curvature of the first cartan - egg domain
域的全纯截曲率 - The characterization of moebius sectional curvature in unit sphere
截曲率的内蕴性 - 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。 - 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。