Volume 13, Issue 2 (10-2018)                   IJMSI 2018, 13(2): 59-70 | Back to browse issues page

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Mohammadpouri A, Pashaie F, Tajbakhsh S. L_1-Biharmonic Hypersurfaces in Euclidean Spaces with Three Distinct Principal Curvatures. IJMSI. 2018; 13 (2) :59-70
URL: http://ijmsi.ir/article-1-816-en.html

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.

Type of Study: Research paper | Subject: Special

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