Totally Real Minimal Submanifolds in a Quaternion Projective Space

51.IntroductionAquaternionKaehlermanifoldisdefinedasa4m-dimensionalRiemannianmanifoldwhoseholonomygroupiscontainedinSp(m).Sp(1)withtheadditionalconditionform=lthatitisaself-dualEinsteinspace.AquaternionprojectivespaceQP:)isaquaternionKeahlermanifoldwithconstantquaternionsectionalcurvaturec>O.AcomplexprojectivespaceCP2)withconstantholomorphicsectionalcurvatureccanbeisometricallyimbeddedinQP:)asatthtallygeodesicsubmanifold.LetMbeannsidimensionalRiemannianmanifoldander:M-Qer).-.'an1sometr1…     

A Remark on Concircularly Flat Totally Real Minimal Submanifolds in CP^n

Let M be a concircularly fiat totally real minimal submanifold in CP4. The infimum Vm of the volume V （M） of M is obtained, also the necessary and sufficient conditions of ＂V（M）=Vm＂ is given.     

Characterization of Totally Geodesic Totally Real 3-dimensional Submanifolds in the 6-sphere

In this paper, we study Lagrangian submanifolds of the nearly Kaehler 6-sphere. We derive a pinching result for the Ricci curvature of such submanifolds thus providing a characterisation of the totally geodesic submanifold. Our pinching result improves a previous result obtained by H. Li.     

复射影空间的2-调和全实子流形

研究了复射影空间中2-调和全实子流形,得到了这类子流形的一个积分公式,讨论了伪脐条件下的情形,通过计算第二基本形式模长平方的Laplacian得到一个刚性定理.     

2—Harmonic Curves Isometrially Immersed in a Surfaee

In this paper,the author proves the necessary and sufficient condition for the existence of 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface N∪→IE^3.     

关于局部对称空间中2-调和子流形

本文研究局部对称完备黎曼流形中的紧致2－调和子流形，得到了这类流形第二基本模式长平方的Pinching定理及推广的J．Simons型积分不等式。     

关于四元射影空间中的全实2-调和子流形

利用了活动标架法对四元射影空间QPnc中全实2-调和子流形进行了研究,获得了这类子流形成为全实极小子流形的刚性定理,推广了相关文献中的积分不等式．     

2—调和映照的复合映照

本文研究了Ricmann流形间2—调和映照的复合映照的性质及其应用.按照J.Eells和L.Lemaire在文献[1]中的设想,姜国英在[2]中通过计林某一泛函数的第一、二变分的方法,探讨了Riemann流形间的2—调的映照f:M→N,它的张力场τ(f)满足方程:(?)其中{e_k}为M的局部标准正交林架场.A^*A是向量丛f^-1TN上的迹Laplace算子,R^N是N的曲率算子.当M紧致时,2—调和映照f恰是使2—能量泛函(?)取临界值的映射.显然,它是调和映照的一种推广.本文研究了Ricmann流形间2—调和映照的复含映照的一个性质,并给出了它的应用.     

Compact Maximal Space-like Submanifolds in a Pseudo-Riemannian Spacetime Sp^m＋p

This paper concerns space-like submanifolds in a pseudo-Riemannian space-time Spm p(?)Epm p 1(p≥1), and proves that connected compact maximal space-like submanifolds in a pseudo-Riemannian spacetime Spm p(?)Epm p 1(p≥1) must be totally umbilical, and also totally geodesic. Particularly, when p = 1, our result is just Montiel's in case of H = 0.     

Quasi—Einstein Hypersurfaces in a Hyperbolic Space

§1.　IntroductionLetRijbethecomponentsofRiccitensorofann-dimensionalRiemannianmanifoldM.IfRij=Agij Bξiξj,　(i,j=1,2,…,n)(1.1)whereξisanunitvectorfield,thenMiscalledaquasi-EinsteinmanifoldanddenotedbyQE(ξ).Ifξisanisotropicvectorfield,thenMiscalledageneralizedquasi-Einsteinmanifold.Intheequality(1.1),AandBarescalarfunctions.WeknowQE(ξ)manifoldisEinsteinwhenB≡0.Especially,if〈ξ,ξ〉=e=±1,thenQE(ξ)iscalledanormalquasi-Einsteinmani-fold.Itiseasytoknowfrom[1]and[2]:Rij=R-Tn-1…     

复空间形式中全实2-调和子流形

本文研究了复空间形式中的全实2-调和子流形,获得了关于此类子流形的一些性质和一个Simons型积分不等式,并研究了其Pinching现象.     

复射影空间中的完备全实伪脐子流形

Let Mn be a totally real pseudo-umbilical submanifold in a complex projective space CPn＋p. In this paper, we study the position of completeness of Mn. By choosing a suitable frame field, we obtain a rigidity theorem such that Mn becomes totally umbilical submanifold and improve the related results.     

关于复射影空间中的全实伪脐子流形

设$M^n$是复射影空间${\bf C}P^{n+p}$中的全实子流形. 本文研究$M^n$的平行脐性法向量场在法丛中的位置. 在$p>0$的情形通过选取合适的标架场, 得到具有平行平均曲率向量的全实伪脐子流形关于第二基本形式模长平方的一个Pinching定理.     

四元数射影空间的全实伪脐子流形

给出了四元数射影空间的紧致全实伪脐子流形的关于第二基本形式长度的一个Ｐｉｎｃｈｉｎｇ定理．     

复射影空间的实2-调和超曲面

本文研究了复射影空间中的实２－调和超曲面和实极小超曲面之间的关系,推广了Ｌａｗｓｏｎ Ｈ．Ｂ和Ｋｏｎ Ｍ．关于实极小超曲面的Ｐｉｎｃｈｉｎｇ结果     

Totally Real Submanifolds in a Quaternion Space Form

In this paper, we prove a theorem for n-dimensional totally real minimal submanifold immersed in quaternion space form.     

复射影空间中法丛平坦的全实伪脐子流形

该文证明了复射影空间中两种类型的法丛平坦全实伪脐子流形必是极小的,并在紧致的情形确定了它们的具体形状．此外,还说明了复射影空间中的全实全脐子流形一定不是法丛平坦的.     

复射影空间中法丛平坦的全实迷向子流形

证明了复射影空间中两种类型法丛平坦的全实迷向予流形必是极小的，并在紧致的情形确定了它们的具体形状．