On biharmonic hypersurfaces of three curvatures in Minkowski 5-space

Authors

  • Firooz Pashaie Deptartment of Mathematics, Faculty of Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran.
  • Naser Tanoomand-khooshmehr Deptartment of Mathematics, Faculty of Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran.
  • Asghar Rahimi Deptartment of Mathematics, Faculty of Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran.
  • Leila Shahbaz Deptartment of Mathematics, Faculty of Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran.

Keywords:

Lorentz hypersurface, nite type, Lk-biharmonic, k-minimal.

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 variationof 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 \Delta and by a famous conjecture due to Bang-Yen Chen each \Delta-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.

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Published

2023-02-04

Issue

Vol. 17

Section

Vol. 17, No. 1, (2023)

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