AU - Mohammadpouri, A.
AU - Pashaie, F.
AU - Tajbakhsh, S.
TI - $L_1$-Biharmonic Hypersurfaces in Euclidean Spaces with Three Distinct Principal Curvatures
PT - JOURNAL ARTICLE
TA - IJMSI
JN - IJMSI
VO - 13
VI - 2
IP - 2
4099 - http://ijmsi.ir/article-1-816-en.html
4100 - http://ijmsi.ir/article-1-816-en.pdf
SO - IJMSI 2
ABĀ - 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.
CP - IRAN
IN - Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
LG - eng
PB - IJMSI
PG - 59
PT - Research paper
YR - 2018