On Some L_r-Biharmonic Euclidean Hypersurfaces
Journal Title: Journal of Mathematics and Applications - Year 2016, Vol 39, Issue
Abstract
In decade eighty, Bang-Yen Chen introduced the concept of biharmonic hypersurface in the Euclidean space. An isometrically immersed hypersurface x : M^n → E^{n+1} is said to be biharmonic if ∆^2x = 0, where ∆ is the Laplace operator. We study the L_r-biharmonic hypersurfaces as a generalization of biharmonic ones, where L_r is the linearized operator of the (r + 1)th mean curvature of the hypersurface and in special case we have L_0 = ∆. We prove that L_r-biharmonic hypersurface of L_r-finite type and also L_r-biharmonic hypersurface with at most two distinct principal curvatures in Euclidean spaces are r-minimal.
Authors and Affiliations
Akram Mohammadpouri, Firooz Pashaie
Keywords
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