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- W2052287732 abstract "In this article, we study $L_k$-finite-type hypersurfaces $M^n$ of a hyperbolic space $mathbb{H}^{n+1}subsetmathbb{R}^{n+2}_1$, for $kgeq 1$. In the 3-dimensional case, we obtain the following classification result. Let $psi:M^3rightarrowmathbb{H}^{4}subsetmathbb{R}^5_1$ be an orientable hypersurface with constant $k$-th mean curvature $H_k$, which is not totally umbilical. Then $M^3$ is of $L_k$-2-type if and only if $M^3$ is an open portion of a standard Riemannian product $mathbb{H}^1(r_1)timesmathbb{S}^{2}(r_2)$ or $mathbb{H}^2(r_1)timesmathbb{S}^{1}(r_2)$, with $-r_1^2+r_2^2=-1$. In the $n$-dimensional case, we show that a hypersurface $M^nsubsetmathbb{H}^{n+1}$, with constant $k$-th mean curvature $H_k$ and having at most two distinct principal curvatures, is of $L_k$-2-type if and only if $M^n$ is an open portion of a Riemannian product $mathbb{H}^m(r_1)timesmathbb{S}^{n-m}(r_2)$, with $-r_1^2+r_2^2=-1$, for some integer $min{1,dots,n-1}$. In the case $k=n-1$ we drop the condition on the principal curvatures of the hypersurface $M^n$, and prove that if $M^nsubsetmathbb{H}^{n+1}$ is an orientable $H_{n-1}$-hypersurface of $L_{n-1}$-2-type then its Gauss-Kronecker curvature $H_{n}$ is a nonzero constant." @default.
- W2052287732 created "2016-06-24" @default.
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- W2052287732 date "2015-01-01" @default.
- W2052287732 modified "2023-09-26" @default.
- W2052287732 title "$L_k$-2-TYPE HYPERSURFACES IN HYPERBOLIC SPACES" @default.
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- W2052287732 doi "https://doi.org/10.11650/tjm.19.2015.4603" @default.
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