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http://dx.doi.org/10.4134/BKMS.b150401

HYPERSURFACES IN 𝕊4 THAT ARE OF Lk-2-TYPE  

Lucas, Pascual (Departamento de Matematicas Universidad de Murcia Campus de Espinardo)
Ramirez-Ospina, Hector-Fabian (Departamento de Matematicas Universidad Nacional de Colombia)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.3, 2016 , pp. 885-902 More about this Journal
Abstract
In this paper we begin the study of $L_k$-2-type hypersurfaces of a hypersphere ${\mathbb{S}}^{n+1}{\subset}{\mathbb{R}}^{n+2}$ for $k{\geq}1$ Let ${\psi}:M^3{\rightarrow}{\mathbb{S}}^4$ be an orientable $H_k$-hypersurface, which is not an open portion of a hypersphere. Then $M^3$ is of $L_k$-2-type if and only if $M^3$ is a Clifford tori ${\mathbb{S}}^1(r_1){\times}{\mathbb{S}}^2(r_2)$, $r^2_1+r^2_2=1$, for appropriate radii, or a tube $T^r(V^2)$ of appropriate constant radius r around the Veronese embedding of the real projective plane ${\mathbb{R}}P^2({\sqrt{3}})$.
Keywords
linearized operator $L_k$; $L_k$-finite-type hypersurface; higher order mean curvatures; Newton transformations;
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