عنوان مجله
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Sahand Communications in Mathematical Analysis
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چکیده
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Biharmonic surfaces in Euclidean space E^3 are firstly
studied from a differential geometric point of view by Bang-Yen
Chen, who showed that the only biharmonic surfaces are minimal
ones.
,0=A surface x : M^2 ---> E^3 is called biharmonic if Δ^2x -where Δ is the Laplace operator of M^2. We study the L_k-
biharmonic spacelike hypersurfaces in the 4-dimentional pseudo-
Euclidean space E^4_1
with an additional condition that the principal
curvatures of M^3 are distinct. A hypersurface x : M^3 ---> E^4 is called
L_k-biharmonic if
L_k x = 0 (for k = 0; 1; 2), where Lk is the lin-
earized operator associated to the r-th variation of (k+1)-th mean
curvature of M^3. Since L0 = Δ, the matter of Lk-biharmonicity is
a natural generalization of biharmonicity. On any Lk-biharmonic
spacelike hypersurfaces in E41
with distinct principal curvatures, by,
assuming Hk to be constant, we get that Hk+1 is constant. Fur-
thermore, we show that Lk-biharmonic spacelike hypersurfaces in
E41
with constant Hk are k-maximal.
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