首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 156 毫秒
1.
局部对称共形平坦黎曼流形中带有平坦法丛的子流形   总被引:1,自引:0,他引:1  
设M~(n p)是n p维共形平坦黎曼流形,且它的黎曼张量R_(tjkl)之共变导微▽R_(tjkl)=0,则称M~(n p)为局部对称共形平坦黎曼流形。 本文证得:若V~n(n≥2)是局部对称共形平坦黎曼流形M~(n p)的n维紧致无边子流形,它具有平坦法丛,若V~n在任一点上的截面曲率均大于T_c-t_c/2(n p-2),这里T_c、t_c分别是M~(n p)的Ricci曲率在该点的上、下确界,则V~n一定是M~(n p)的n 1维全测地子流形M~(n 1)之超曲面。  相似文献   

2.
孙弘安 《数学季刊》1991,6(3):67-72
本文目的在于建立共形平坦黎曼流形中子流形的数量曲率截面曲率间关系的几个不等式,在流形是常曲率的情况下,这些不等式改进了B.Y.Chen和M.Okumura的结果。§1.基本公式和引理设M~(n+p)是一个n+p维的共形平坦黎曼流形,V~n是M~(n+p)的n维子流形。在M~(n+p)中选取局  相似文献   

3.
设M~(n+2)是■+■维局部对称的共形平坦■曼流形,M~n是它的紧致的n维极小子流形(n≥4).本文证明,若M~n的每点各方向的(?)曲率的下确界Q>(n-2)K,其中K是M~(n+p)在该点的截面曲率的上确界,则M~n是全测地的,且有正常数截面曲率.  相似文献   

4.
局部对称共形平坦黎曼流形中紧致子流形的一个刚性定理   总被引:3,自引:0,他引:3  
本文研究局部对称共形平坦黎曼流形N^n p(p≥2)中具有平行平均曲率向量的紧致子流形M^n的余维可约性问题,在n≥8的条件下得到了最佳拼挤常数。  相似文献   

5.
该文研究了局部对称共形平坦空间中具有常数量曲率的紧致子流形,证明了这类子流形的某些内蕴刚性定理.  相似文献   

6.
局部对称共形平坦黎曼流形中的紧致子流形   总被引:1,自引:0,他引:1  
张剑锋 《数学杂志》2004,24(1):7-12
本文研究局部对称共形平坦黎曼流形中具有平行平均曲率向量的紧致子流形的性质,通过一个代数不等式的证明,改进了已有的结果.  相似文献   

7.
本文研究局部对称共形平坦黎曼流形中紧致极小子流形,得到了这类子流形第二基本形式模长平方关于外围空间Ricci曲率的—个拼挤定理,推广了文[1]中的结果.  相似文献   

8.
局部对称黎曼流形中具有平行平均曲率向量的子流形   总被引:1,自引:0,他引:1  
吴庆琼  钟定兴 《数学研究》2001,34(3):276-281
设Nn+p是截面曲率KN满足的n+p维局部对称完备黎曼流形,p≥2.M是Nn+p的具有平行平均曲率向量的n维紧致子流形.本文讨论了这类子流形关于第二基本形式模长平方的积分不等式及其Pinching问题.  相似文献   

9.
郭彩虹 《数学研究》2007,40(1):66-71
研究局部对称共形平坦黎曼流形N^n+p(p≥2)中具有平等平均曲率向量的紧致子流形M^n的余维可约性问题,在n≥8的条件下得到了量佳拼挤常数.  相似文献   

10.
本文首先将常曲率黎曼流形中B.Y.Chen和M.Okumura关于数量曲率和截面曲率关系间的一个著名不等式推广到环绕空间是局部对称共形平坦黎曼流形的情形.作为应用,较简捷地将M.Okumura在[2],[3]中的结果推广到这种环绕空间中法联络是平坦的子流形上去.  相似文献   

11.
李伟勋 《数学研究》2009,42(4):427-429
证明了指数型超椭圆方程x^2=p^2m-p^m+n+1无解(x,p,m,n),其中x,m,n∈N^+,m〉n〉1,p∈P.上述结果部分解决了组合论中关于可逆Abel差集的Ma猜想.  相似文献   

12.
The Properties of submanifolds in a Bochner-Kaehler manifold have been studied mainly in the cases that the submanifolds are totally real by Yano, K., Houh, 0. S. and others. The main purpose of the present paper is to study whether the condition for the submanifold to be totolly real in their theorems is necessary, and to prove some theorems which are analogous to those mentioned above. A submanifold M^n of Kaehlerian manifold M^2m is called totally real or antiinvariant,if each tangent space of M^n is mapped into the normal space by the complex structure $\[{F_{\nu \mu }}\]$ of M^2m. Similarly, a submanifold M^n of Kaehlerian manifold M^2m is called anti-in variant with respect to L', if each tangent space of M^n is mapped into the normal space by the operator L' of M^2m. We obtain: (1) A necessary and sufficient condition for a totally umbilical submanifold M^n, n>3, in a Boohner-Kaehler manifold M^2m to be conformally flat is that the submanifold M^n is either a totally real submanifold or an anti-invariant submanifold with respect to L'. (2) Let M^n be the submanifold immersed in a Boohner-Kaehler manifold M^2m. If each tangent vector of M^n is Ricci principal direction and Ricci principal curvature $\[{\rho _h}\]$ does not equal $[\frac{{\tilde K}}{{4(m + 1)}}\]$ , then the anti-invariant submanifold with respect to L^' coincides with the totally real submanifold. (3) Let M^n be a totally umbilical submanifold immersed in a Boohner-Kaehler manifold M^2m If M^n is a totally real submanifold or an anti-invariant submanifold,then the sectional curvature of Mn is given by $[\rho (u,v) = \frac{1}{8}(\tilde K(u) + \tilde K(v)) + \sum\limits_{x = n + 1}^{2m} {{H^2}} ({e_x})\]$(A) where H(e_x) =H_x. Conversely, if the sectional curvature of M^n satisfying the condition mentioned in (2) is given by (A) for any two orthonormal tangent vectors u^\alpha and $v^\alpha$ then M^n is a totally real submanifold.  相似文献   

13.
This paper deals with the p-harmonic function on a complete non-compact submanifold M isometrically immersed in an (n + k)-dimensional complete Riemannian manifold (M) of non-negative (n-1)-th Ricci curvature.The Liouville type theorem about the p-harmonic map with finite Lq-energy from complete submanifold in a partially nonnegatively curved manifold to non-positively curved manifold is also obtained.  相似文献   

14.
徐森林  宋冰玉 《数学研究》2005,38(3):238-242
研究了球面Sn+p(c)子流形Mn的Pinching定理,证明了当s<2√n-1c时,Mn(n>3)与n维球面同胚.  相似文献   

15.
对任意正整数n,我们定义数列主要目的是利用初等及组合方法研究N~2的数字和的计算问题,并给出一个有趣的计算公式.即就是证明了当n=9k+i时,N~2的数字和为M(N~2)=81k+i~2,其中k为非负整数,1≤i≤9.作为应用,容易回答2012年匈牙利数学竞赛中提出的这样一个问题:问自然数、的表示式中第73项的数字是多少?不难推出的第73项的数字是0,第74项是2,第75项是3等等.  相似文献   

16.
研究了$(n+p)$维双曲空间$\mathbb{H}^{n+p}$中完备非紧子流形的第一特征值的上界.特别地,证明了$\mathbb{H}^{n+p}$中具有平行平均曲率向量$H$和无迹第二基本形式有限$L^q(q\geq n)$范数的完备子流形的第一特征值不超过$\frac{(n-1)^2(1-|H|^2)}{4}$,和$\mathbb{H}^{n+1}(n\leq5)$中具有常平均曲率向量$H$和无迹第二基本形式有限$L^q(2(1-\sqrt{\frac{2}{n}})相似文献   

17.
This paper deals with the p-harmonic function on a complete non-compact submanifold M isometrically immersed in an(n + k)-dimensional complete Riemannian manifold M of non-negative(n-1)-th Ricci curvature. The Liouville type theorem about the p-harmonic map with finite L~q-energy from complete submanifold in a partially nonnegatively curved manifold to non-positively curved manifold is also obtained.  相似文献   

18.
该文证明了de Sitter空间中具有平行平均曲率向量的常数量曲率完备类空子流形,如果其法联络是平坦的,且M的截面曲率小于0,或M的第二基本形式模长平方‖σ‖相似文献   

19.
In Euclidean geometry, for a real submanifold M in E n+a , M is a piece of E n if and only if its second fundamental form is identically zero. In projective geometry, for a complex submanifold M in CP n+a , M is a piece of CP n if and only if its projective second fundamental form is identically zero. In CR geometry, we prove the CR analogue of this fact in this paper.  相似文献   

20.
A non-totally-geodesic submanifold of relative nullity n — 1 in a symmetric space M is a cylinder over one of the following submanifolds: a surface F 2 of nullity 1 in a totally geodesic submanifold N3 ? M locally isometric to S 2(c) × ? or H 2(c) × ?; a submanifold F k+1 spanned by a totally geodesic submanifold F k(c) of constant curvature moving by a special curve in the isometry group of M; a submanifold F k+l of nullity k in a flat totally geodesic submanifold of M; a curve.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号