緊子流形 的英文怎麼說
中文拼音 [jǐnziliúxíng]
緊子流形
英文
compact submanifold-
Compact maximal spacelike submanifolds in a de sitter space
空間中的緊致極大類空子流形Give me the gift of a grip top sock : a drip - drape, ship - shape, tip - top sock
送我一對有緊襪帶的襪子：懸掛狀的、船形的、品質一流的襪子。A compact minimal submanifold of sasakian space form
空間形式中的緊致極小子流形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緊致全實偽臍子流形m ~ n ，得到了（ ? ）如果m ~ n在其點x的截面曲率的下確界函數k （ x ）滿足條件：則m ~ n是全臍的（ ? ）如果m ~ n在其點x的ricci曲率的下確界函數q （ x ）滿足條件：則m ~ n是全臍的。 （ ? ）如果m在m中的第二基本形式h長度的平方滿足條件：則m ~ n是全臍的。This paper contains three chapters. we discuss the pinching problems on the length of the second fundamental form of compact space - like submanifolds mn with unit parallel mean curvature vector in the de sitter space spn + p. in particular, a sufficient condition for mn with constant scalar curvature to be totally umbilical is given
討論desitter空間s _ p ~ （ n + p ）中具有平行的單位平均曲率向量的緊致類空子流形m ~ n的第二基本形式長度拼擠問題，給出了具有常數量曲率的這種子流形是全臍球面的一個充分條件。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。The compact minimal submanifold of a locally symmetric and conformally flat riemannian manifold are studied, and obtain the following intrinsic rigidity theorem. i. e. if m be a compact minimal submanifold of a locally symmetric and conformally flat riemannian manifold n ( superscript n + p )
摘要研究了局部對稱共形平坦黎曼流形的緊致極小子流形，即設m是局部對稱共形平坦黎曼流形的n維緊致極小子流形，得到了這種子流形的若干內蘊剛性積分不等式，給出了流形全測地的限制條件。In this paper, the authors give the globally classfication of the maximal totally geodesic submanifolds with maximal rank of normal riemannian symmetric spaces by computing the fundamental group
摘要通過計算全測地子流形的基本群，確定了緊正規黎曼對稱空間的極大的極大秩全測地子流形的整體分類。分享友人