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
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 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
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.
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.
