%0 Journal Article
%A Mohammadpouri, A.
%A Pashaie, F.
%A Tajbakhsh, S.
%T $L_1$-Biharmonic Hypersurfaces in Euclidean Spaces with Three Distinct Principal Curvatures
%J Iranian Journal of Mathematical Sciences and Informatics
%V 13
%N 2
%U http://ijmsi.ir/article-1-816-en.html
%R
%D 2018
%K Linearized operators $L_r$, $L_1$-biharmonic hypersurfaces, $1$-minimal,
%X Chen's biharmonic conjecture is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we consider an advanced version of the conjecture, replacing $Delta$ by its extension, $L_1$-operator ($L_1$-conjecture). The $L_1$-conjecture states that any $L_1$-biharmonic Euclidean hypersurface is 1-minimal. We prove that the $L_1$-conjecture is true for $L_1$-biharmonic hypersurfaces with three distinct principal curvatures and constant mean curvature of a Euclidean space of arbitrary dimension.
%> http://ijmsi.ir/article-1-816-en.pdf
%P 59-70
%& 59
%!
%9 Research paper
%L A-10-1770-1
%+
%G eng
%@ 1735-4463
%[ 2018