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1.
设M是n维双曲空间Hn的一个k维的逆紧浸入完备极小子流形,如果M的渐近边界是一个k-1维球面,则M是一个k维的全测地子流形.  相似文献   

2.
徐森林  黄正 《应用数学》1999,12(1):72-75
本文通过具有良好性质的子流形的存在性,证明了一类流形的一个刚性定理,并得到形如Bonnet-Myers定理的推论.我们还指出,在主要定理中全测地子流形的条件一般不能减弱为极小子流形.  相似文献   

3.
罗治国 《数学学报》1995,38(3):400-405
本文讨论四元射影空间的全复子流形,证明了四元射影空间的正截面曲率紧致全复子流形一定是全测地的。  相似文献   

4.
Sasakian子流形的谱几何   总被引:1,自引:1,他引:0  
周振荣 《数学杂志》2000,20(1):83-86
本文讨论了 Sasakian子流形的谱几何,获得了复 Quadric上圆周丛以及全测地子流形的谱特征.  相似文献   

5.
局部对称Bochner-Kaehler流形及其Kaehler子流形   总被引:3,自引:0,他引:3  
本文给出局部对称的Bochner-Kaehler流形的Riemann结构以及它的Kaehler子流形为全测地子流形的几个Pinching条件,推广了关于复射影空间的Kaehler子流形的相应定理。  相似文献   

6.
关于浸入的Gauss映照和调和映照的几个结果   总被引:1,自引:0,他引:1  
Obata 在[1]中将欧氏空间中子流形 Gauss 映照的概念推广到单连通完备常曲率空间中的子流形上,并得到了若干结果。这样,利用欧氏空间或球面中子流形的 Gauss 映照来研究子流形性质的方法日趋常见(参见[2],[5],[6],[7])[6]中证明了球面中子流形的 Gauss 映照为全测地时,必为全测地子流形,作为其推广,本文证明了球面中子流  相似文献   

7.
本文研究了殆Kaehler流形中CR子流形的上同调、CR子波形的分布D及其正交补D⊥的维数大于1的时候,近Kaehler流形中每个全脐非平凡的CR子流形一定是全测地的。最后得到:如果M^~是具有H^~B>0的近Kaehler流形,那么M^~不允许有混合叶层非凡的CR子流形。  相似文献   

8.
球空间S^n+p(C)中的紧致极小子流形   总被引:4,自引:0,他引:4  
纪永强 《数学杂志》1990,10(4):391-396
设 M~n 是常曲率空间 S~(n+p)(c)的紧致极小子流形,设 K 和 Q 分别是 M~n 上每点各方向截面曲率和 Ricci 曲率的下确界,R 是 M~n 的数量曲率,本文利用 M~n 的内在量 KQ和 R,给出球空间中紧致极小子流形是全测地子流形的六个充分条件。  相似文献   

9.
朱富海  梁科 《中国科学A辑》2004,34(2):140-145
给出了非紧型对称空间的极大秩全测地子流形的分类, 紧型的相应结果可利用对偶性得到.  相似文献   

10.
本文决定了经典的紧致黎曼对称空间的一大批全测地子流形,并确定了它们在其包围空间中的稳定性.  相似文献   

11.
We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex homogeneous submanifold of C N must be totally geodesic.  相似文献   

12.
Summary We construct definitely the automorphism group of a Sasakian space form ¯M=E 2m+1 (–3) and study the existence of a totally geodesic invariant submanifold of ¯M tangent to a given invariant subspace in the tangent space of ¯M. We also study the Frenet curves in ¯M under a totally contact geodesic immersion of a contact CR-submanifold into ¯M. The purpose of this paper is to prove a reduction theorem of the codimension for a totally contact geodesic, contact CR-submanifold of ¯M.  相似文献   

13.
We prove that the Hopf vector field is unique among geodesic unit vector fields on spheres such that the submanifold generated by the field is totally geodesic in the unit tangent bundle with Sasaki metric. As an application, we give a new proof of stability (instability) of the Hopf vector field with respect to volume variation using standard approach from the theory of submanifolds and find exact boundaries for the sectional curvature of the Hopf vector field.  相似文献   

14.
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   

15.
§1.IntroductionLetMbeann-dimensionalclosedminimalyimmersedsubmanifoldintheunitsphereSn+p,Sthesequreofthelengthofthesecondfund...  相似文献   

16.
Hijazi and Zhang improved Friedrich’s inequality for non-minimal spin submanifolds. Their proof relies on the non-minimality assumption. We use another method to prove that their theorem holds also for minimal submanifolds. As an application, we show that any Kähler manifold can be embedded as a totally geodesic submanifold of its twistor space and apply the above result.  相似文献   

17.
We prove that a Lagrangian submanifold passes through each point of a symplectic manifold in the direction of arbitrary Lagrangian plane at this point. Generally speaking, such a Lagrangian submanifold is not unique; nevertheless, the set of all such submanifolds in Hermitian extension of a symplectic manifold of dimension greater than 4 for arbitrary initial data contains a totally geodesic submanifold (which we call the s-Lagrangian submanifold) iff this symplectic manifold is a complex space form. We show that each Lagrangian submanifold in a complex space form of holomorphic sectional curvature equal to c is a space of constant curvature c/4. We apply these results to the geometry of principal toroidal bundles.  相似文献   

18.
极小子流形上Laplace算子的谱   总被引:2,自引:0,他引:2  
本文讨论了Sn+p(1)(或CPn+1)中极小子流形上Laplace算子的谱,证明了Sn+p(1)中全测地极小子流形(或CPn+1中Kachler超曲面)是由作用在q-形式上的Laplace算子的谱唯一确定.  相似文献   

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