Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
14
8888
13
en
jalali
1397
7
1
gregorian
2018
10
1
13
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online
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fulltext
en
L_1-Biharmonic Hypersurfaces in Euclidean Spaces with Three Distinct Principal Curvatures
تخصصي
Special
پژوهشي
Research paper
<p>Chen's biharmonic conjecture is well-known and stays open: The only<br>
biharmonic submanifolds of Euclidean spaces are the minimal ones. In<br>
this paper, we consider an advanced version of the conjecture,<br>
replacing Delta by its extension, L_1-operator<br>
(L_1-conjecture). The L_1-conjecture states that any<br>
L_1-biharmonic Euclidean hypersurface is 1-minimal. We prove that<br>
the L_1-conjecture is true for L_1-biharmonic hypersurfaces with<br>
three distinct principal curvatures and constant mean curvature of a<br>
Euclidean space of arbitrary dimension.</p>
Linearized operators L_r, L_1-biharmonic hypersurfaces, 1-minimal
59
70
http://ijmsi.ir/browse.php?a_code=A-10-1770-1&slc_lang=en&sid=1
A.
Mohammadpouri
pouri@tabrizu.ac.ir
10031947532846006507
10031947532846006507
Yes
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
F.
Pashaie
10031947532846006508
10031947532846006508
No
Department of Mathematics, Faculty of Basic Sciences, University of Maragheh.
S.
Tajbakhsh
10031947532846006509
10031947532846006509
No
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.