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$5$-dimensional constant Gauss-Kroneckercurvature hypersurfaces of spheres
Perdomo Oscar 1,Wei Guoxin 2 *
1.Department of Mathematics, Central Connecticut State University, New Britain 06050
2.School of Mathematical Sciences, South China Normal University, Guangzhou 510631
*Correspondence author
#Submitted by
Subject:
Funding: SRFDP （No.Grant No. 20104407120002）, NSFC （No.Grant No. 11371150）
Opened online:20 February 2014
Accepted by: none
Citation: Perdomo Oscar,Wei Guoxin.$5$-dimensional constant Gauss-Kroneckercurvature hypersurfaces of spheres[OL]. [20 February 2014] http://en.paper.edu.cn/en_releasepaper/content/4585284
 
 
Let $Msubset S^{6}$ be a complete orientable hypersurface with constant Gauss-Kronecker curvature $G$. For any $vin R^{7}$, let us define the following two real functions $l_v, f_v:M o R$on $M$ by $l_v(x)=<x,v>$ and $f_v(x)=<u(x),v>$ with $u:M o S^{6}$ a Gauss map of $M$. We show that if $l_v=lambda f_v$ for some nonzero vector $vin R^{7}$ and some real number $lambda$ and $(lambda^2-1)^2+(G^2-1)^2eq 0$, then $M$ is either $S^5(r)$ or $M$ is $S^k(r) imes S^{5-k}(sqrt{1-r^2})$.
Keywords:Pure mathematics; hypersurfaces; Gauss-Kronecker curvature
 
 
 

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