Super minimal surfaces in hyper quadric Q2  

作　　者：Jun WANG Jie FEI 

机构地区：[1]School of Mathematics Sciences and Institute of Mathematics,Nanjing Normal University,Nanjing 210023,China [2]Department of Pure Mathematics,School of Science,Xi'an Jiaotong-Liverpool University,Suzhou 215123,China

出　　处：《Frontiers of Mathematics in China》2020年第5期1035-1046,共12页中国高等学校学术文摘·数学（英文）

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);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).

摘　　要：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.

关 键 词：Hyperquadric superminimal surface totally real HOLOMORPHIC 

分 类 号：O18[理学—数学]