Biharmonic Hypersurfaces in 4-dimensional Space Forms
نویسنده
چکیده
We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.
منابع مشابه
$L_k$-biharmonic spacelike hypersurfaces in Minkowski $4$-space $mathbb{E}_1^4$
Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...
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