L1-BIHARMONIC HYPERSURFACES IN EUCLIDEAN SPACES WITH THREE DISTINCT PRINCIPAL CURVATURES

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MOHAMMADPOURI AKRAM; Pashaie Firooz; TAJBAKHSH SEPIDE

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Journal Paper

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Journal: Iranian Journal of Mathematical Sciences and Informatics Year:2018 | Volume:13 | Issue:2 Page(s): 59-70

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Information Journal Paper

Title

L1-BIHARMONIC HYPERSURFACES IN EUCLIDEAN SPACES WITH THREE DISTINCT PRINCIPAL CURVATURES

Author(s)

MOHAMMADPOURI AKRAM | Pashaie Firooz | TAJBAKHSH SEPIDE | Issue Writer Certificate

Keywords

LINEARIZED OPERATORS L>SUB>1

L1-BIHARMONIC HYPERSURFACES

1-MINIMAL

Abstract

A submanifold Mn of the Euclidean space En+m is said to be biharmonic if its position map x: Mn®En+m satisfies the condition D2x=0, where D stands for the Laplace operator. A well-known conjecture of Bang-Yen Chen says that, the only biharmonic submani-folds of Euclidean spaces are the minimal ones. In this paper, we consider a modified version of the conjecture, replacing D by its extension, L1-operator (namely, L1-conjecture). The L1-conjecture states that any L1-biharmonic Euclidean hyper surface is 1-MINIMAL. We prove that the L1-conjecture is true for L1-biharmonic hyper surfaces with three distinct principal curvatures and constant mean curvature of a Euclidean space of arbitrary dimension.

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References

ON HARMONIC INDEX AND DIAMETER OF UNICYCLIC GRAPHS

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APA: Copy

MOHAMMADPOURI, AKRAM, Pashaie, Firooz, & TAJBAKHSH, SEPIDE. (2018). L₁-BIHARMONIC HYPERSURFACES IN EUCLIDEAN SPACES WITH THREE DISTINCT PRINCIPAL CURVATURES. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 13(2), 59-70. SID. https://sid.ir/paper/310475/en

Vancouver: Copy

MOHAMMADPOURI AKRAM, Pashaie Firooz, TAJBAKHSH SEPIDE. L₁-BIHARMONIC HYPERSURFACES IN EUCLIDEAN SPACES WITH THREE DISTINCT PRINCIPAL CURVATURES. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2018;13(2):59-70. Available from: https://sid.ir/paper/310475/en

IEEE: Copy

AKRAM MOHAMMADPOURI, Firooz Pashaie, and SEPIDE TAJBAKHSH, “L₁-BIHARMONIC HYPERSURFACES IN EUCLIDEAN SPACES WITH THREE DISTINCT PRINCIPAL CURVATURES,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 13, no. 2, pp. 59–70, 2018, [Online]. Available: https://sid.ir/paper/310475/en

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