عنوان مجله
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Functional Analysis, Approximations and Computations
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چکیده
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In this paper, we study on a Riemannian manifold Mn, isometrically immersed by a map
x : M^n → E^{n+1}
in the Minkowski space E^{n+1}_1
where the position map x satisfies the condition L^2_1
x = 0. This
condition, as an extended version of the biharmonicity (defined by Δ^2 x = 0), is called the L_1-biharmonicity
condition, where L_1 stands for the linearized operator of the first variation of 2-th mean curvature of M^n in
E^{n+1}
A well-known conjecture of Bang-Yen Chen says that any biharmonic Euclidean submanifold has to .
be minimal. We discuss an analog of the Chen conjecture, replacing the Laplace operator Δ by L_1. Having
assumed that M^n has at least three distinct principal curvatures and constant ordinary mean curvature, we
prove that it must be 1-maximal.
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