SPACE-LIKE BLASCHKE ISOPARAMETRIC SUBMANIFOLDS IN THE LIGHT-CONE OF CONSTANT SCALAR CURVATURE  

作　　者：Hongru SONG Ximin LIU 宋虹儒;刘西民(School of Mathematical Sciences,Dalian University of Technology,Dalian116024,China)

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian116024,China

出　　处：《Acta Mathematica Scientia》2022年第4期1547-1568,共22页数学物理学报（B辑英文版）

基　　金：supported by Foundation of Natural Sciences of China(11671121,11871197 and 11431009)。

摘　　要：Let E_(s)^(m+p+1) ?R_(s+1)^(m+p+2)(m≥ 2,p≥ 1,0≤s≤p) be the standard(punched)light-cone in the Lorentzian space R_(s+1)^(m+p+2),and let Y:M^(m)→E_(s)^(m+p+1) be a space-like immersed submanifold of dimension m.Then,in addition to the induced metric g on Mm,there are three other important invariants of Y:the Blaschke tensor A,the conic second fundamental form B,and the conic Mobius form C;these are naturally defined by Y and are all invariant under the group of rigid motions on E_(s)^(m+p+1).In particular,g,A,B,C form a complete invariant system for Y,as was originally shown by C.P.Wang for the case in which s=0.The submanifold Y is said to be Blaschke isoparametric if its conic Mobius form C vanishes identically and all of its Blaschke eigenvalues are constant.In this paper,we study the space-like Blaschke isoparametric submanifolds of a general codimension in the light-cone E_(s)^(m+p+1) for the extremal case in which s=p.We obtain a complete classification theorem for all the m-dimensional space-like Blaschke isoparametric submanifolds in Epm+p+1of constant scalar curvature,and of two distinct Blaschke eigenvalues.

关 键 词：Conic Mobius form parallel Blaschke tensor induced metric conic second fundamental form stationary submanifolds constant scalar curvature 

分 类 号：O186.1[理学—数学]