Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. ...Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.展开更多
This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-...This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved.展开更多
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.
In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fu...In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally real submanifold in the complex projective space.展开更多
It has been shown, under certain conditions on the Gauss curvature, every totally real surface of the Cayley projective plane with parallel mean curvature vector is either flat or totally geodesic.
Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame f...Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame field,we obtain a pinching theorem,in the case p>0, for the square of the length of the second fundamental form of a totally real pseudo-umbilical submanifold with parallel mean curvature vector.展开更多
Our purpose is to study the minimal tori in the hyperquadric Q2. Firstly, we obtain a necessary and sufficient condition for the minimal surface in Qn which is also minimal in CPn＋1. Next, we show that this kind of m...Our purpose is to study the minimal tori in the hyperquadric Q2. Firstly, we obtain a necessary and sufficient condition for the minimal surface in Qn which is also minimal in CPn＋1. Next, we show that this kind of minimal surface （neither holomorphic nor anti-holomorphic） with constant curvature in Q2 is part of a flat totally real torus. Finally, we prove that totally real minimal fiat tori in Q2 must be totally geodesic, and we classify all the totally geodesic closed surfaces in Q2.展开更多
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 ...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.展开更多
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 subman...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.展开更多
In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex ...In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex curves in the nearly Kahler S-6 are determined completely.展开更多
We study a superminimal surface M immersed into a hyperquadric Q2 in several cases classified by two global defined functions TX and TY,which were introduced by X.X.Jiao and J.Wang to study a minimal immersion f:M→Q2...We study a superminimal surface M immersed into a hyperquadric Q2 in several cases classified by two global defined functions TX and TY,which were introduced by X.X.Jiao and J.Wang to study a minimal immersion f:M→Q2.In case both TX and TY are not identically zero,it is proved that fis superminimal if and only if f is totally real or io f:M→CP3 is also minimal,where i:Q2→CP^3 is the standard inclusion map.In the rest case that TX=0 or TY=0,the minimal immersion f is automatically superminimal.As a consequence,all the superminimal two-spheres in Q2 are completely described.展开更多
文摘Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.
基金the Natural Science Foundation of Education Committee of Anhui Province(2004kj166zd)Foundation for Younger Teachers of Anhui Normal University(2005xqn01).
文摘This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved.
基金Supported by the NSF of Education Department of Henan Province(20021100002)Supported by the NSF of Education Department of Henan Province(200510475038)
文摘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.
文摘In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally real submanifold in the complex projective space.
文摘It has been shown, under certain conditions on the Gauss curvature, every totally real surface of the Cayley projective plane with parallel mean curvature vector is either flat or totally geodesic.
基金Foundation item： the Natural Science Foundation of Anhui Educational Committee （No. KJ2008A05ZC） the Younger Teachers of Anhui Normal University （No. 2005xqn01）.
文摘Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame field,we obtain a pinching theorem,in the case p>0, for the square of the length of the second fundamental form of a totally real pseudo-umbilical submanifold with parallel mean curvature vector.
基金supported by National Natural Science Foundation of China(Grant Nos.11071248 and 11226079)Program of Natural Science Research of Jiangsu Higher Education Institutions of China(Grant No.12KJD110004)
文摘Our purpose is to study the minimal tori in the hyperquadric Q2. Firstly, we obtain a necessary and sufficient condition for the minimal surface in Qn which is also minimal in CPn＋1. Next, we show that this kind of minimal surface （neither holomorphic nor anti-holomorphic） with constant curvature in Q2 is part of a flat totally real torus. Finally, we prove that totally real minimal fiat tori in Q2 must be totally geodesic, and we classify all the totally geodesic closed surfaces in Q2.
基金Supported by the Natural Science Foundation of Anhui Educational Committee (Grant No. KJ2011Z149)
文摘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.
基金Research partially supported by the Ministry of Science and Environmental Protectipn of Serbia, Project 1646Research partially supported by EGIDE, Pavle Savic 07945VC(France)
文摘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.
基金Project supported by the National Natural Science Foundation of China (10271106)
文摘In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex curves in the nearly Kahler S-6 are determined completely.
基金supported by the National Natural Science Foundation of China(Grant No.11301273)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(17KJA110002)+2 种基金the Natural Science Foundationof Jiangsu Province(BK20181381)The second author was supported by the NationalNatural Science Foundation of China(Grant No.11401481)the Research Enhancement Fund and Continuous Support Fund of Xi'an Jiaotong-Liverpool University(REF-18-O1-03,RDF-SP-43).
文摘We study a superminimal surface M immersed into a hyperquadric Q2 in several cases classified by two global defined functions TX and TY,which were introduced by X.X.Jiao and J.Wang to study a minimal immersion f:M→Q2.In case both TX and TY are not identically zero,it is proved that fis superminimal if and only if f is totally real or io f:M→CP3 is also minimal,where i:Q2→CP^3 is the standard inclusion map.In the rest case that TX=0 or TY=0,the minimal immersion f is automatically superminimal.As a consequence,all the superminimal two-spheres in Q2 are completely described.
