Let(e)m+p+1s(C)Rm+p+2s+1(m≥2,p≥1,0≤s≤p)be the standard(punched)light-cone in the Lorentzian space Rm+p+2s+1,and let Y:Mm →(e)m+p+1s 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 M?bius form C;these are naturally defined by Y and are all invariant under the group of rigid motions on e'm+p+1s.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 M?bius 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)m+p+1s 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(e)m+p+1p of constant scalar curvature,and of two distinct Blaschke eigenvalues.

School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China

[1]Hongru SONG;Ximin LIU-.SPACE-LIKE BLASCHKE ISOPARAMETRIC SUBMANIFOLDS IN THE LIGHT-CONE OF CONSTANT SCALAR CURVATURE)[J].数学物理学报（英文版）,2022(04):1547-1568

BLASCHKE,ISOPARAMETRIC,SUBMANIFOLDS,CONSTANT,SCALAR,CURVATURE,m+p+1s,Rm+p+2s+1,isoparametric,codimension,m+p+1p

SPACE,LIKE,IN,THE,LIGHT,CONE,OF,Let,be,standard,punched,light,cone,Lorentzian,space,Mm,like,immersed,Then,addition,induced,there,are,three,other,important,invariants,Blaschke,tensor,conic,second,fundamental,form,bius,these,naturally,defined,by,under,group,rigid,motions,In,particular,complete,system,was,originally,shown,Wang,case,which,said,its,vanishes,identically,eigenvalues,constant,this,paper,we,study,submanifolds,general,extremal,We,obtain,classification,theorem,dimensional,scalar,curvature,two,distinct

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