2024 : 11 : 13
Asghar Rahimi

Asghar Rahimi

Academic rank: Professor
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Education: PhD.
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Research

Title
On Biharmonic Hypersurfaces of Three Curvatures in Minkowski 5-Space
Type
JournalPaper
Keywords
Lorentz hypersurface, finite type, L_k-biharmonic, k-minimal.
Year
2023
Journal Journal of mathematical extension
DOI
Researchers Firooz Pashaie ، ، Asghar Rahimi ، Leila Shahbaz

Abstract

In this paper, we study the L_k-biharmonic Lorentzian hypersurfaces of the Minkowski 5-space M^5, whose second fundamental form has three distinct eigenvalues. An isometrically immersed Lorentzian hypersurface, x : M^4_1 →M^5, is said to be L_k-biharmonic if it satisfies the condition (L_k)^2 x = 0, where L_k is the linearized operator associated to the 1st variation of the mean curvature vector field of order (k + 1) on M^4_1. In the special case k = 0, we have L_0 is the well-known Laplace operator ∆ and by a famous conjecture due to Bang-Yen Chen each ∆-biharmonic submanifold of every Euclidean space is minimal. The conjecture has been affirmed in many Riemannian cases. We obtain similar results confirming the L_k-conjecture on Lorentzian hypersurfaces in M^5 with at least three principal curvatures.