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

XML Print

Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

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

Add your comments about this article : Your username or Email:

© 2018 All Rights Reserved | Iranian Journal of Mathematical Sciences and Informatics

Designed & Developed by : Yektaweb