عنوان مجله
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Journal of Mathematics and Applications
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چکیده
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Abstract: In decade eighty, Bang-Yen Chen introduced the concept
of biharmonic hypersurface in the Euclidean space. An isometrically im-
mersed hypersurface x : Mn ! En+1 is said to be biharmonic if 2x = 0,
where is the Laplace operator. We study the Lr-biharmonic hypersur-
faces as a generalization of biharmonic ones, where Lr is the linearized
operator of the (r + 1)th mean curvature of the hypersurface and in spe-
cial case we have L0 = . We prove that Lr-biharmonic hypersurface
of Lr-nite type and also Lr-biharmonic hypersurface with at most two
distinct principal curvatures in Euclidean spaces are r-minimal.
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