This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal sur...This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.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Supported by the National Natural Science Fundation of China.
文摘This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.
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.
