HYPERSURFACES IN 𝕊4 THAT ARE OF Lk-2-TYPE

Title & Authors
HYPERSURFACES IN 𝕊4 THAT ARE OF Lk-2-TYPE
Lucas, Pascual; Ramirez-Ospina, Hector-Fabian;

Abstract
In this paper we begin the study of $\small{L_k}$-2-type hypersurfaces of a hypersphere $\small{{\mathbb{S}}^{n+1}{\subset}{\mathbb{R}}^{n+2}}$ for $\small{k{\geq}1}$ Let $\small{{\psi}:M^3{\rightarrow}{\mathbb{S}}^4}$ be an orientable $\small{H_k}$-hypersurface, which is not an open portion of a hypersphere. Then $\small{M^3}$ is of $\small{L_k}$-2-type if and only if $\small{M^3}$ is a Clifford tori $\small{{\mathbb{S}}^1(r_1){\times}{\mathbb{S}}^2(r_2)}$, $r^2_1+r^2_2 Keywords linearized operator $\small{L_k}$;$\small{L_k}$-finite-type hypersurface;higher order mean curvatures;Newton transformations; Language English Cited by References 1. L. J. Alias, A. Ferrandez, and P. Lucas, Surfaces in the 3-dimensional LorentzMinkowski space satisfying${\Delta}_{x}$= A$_{x}$+ B, Pacific J. Math. 156 (1992), no. 2, 201-208. 2. L. J. Alias, A. Ferrandez, and P. Lucas, Submanifolds in pseudo-Euclidean spaces satisfying the condition${\Delta}x$= Ax+B, Geom. Dedicata 42 (1992), no. 3, 345-354. 3. 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