Abstract
We prove that every biharmonic hypersurface having constant higher order mean curvature Hr for r > 2 in a space form M5(c) is of constant mean curvature. In particular, every such biharmonic hypersurface in 𝕊5(1) has constant mean curvature. There exist no such compact proper biharmonic isoparametric hypersurfaces M in 𝕊5(1) with four distinct principal curvatures. Moreover, there exist no proper biharmonic hypersurfaces in hyperbolic space ℍ5 or in E5 having constant higher order mean curvature Hr for r > 2.
Communicated by: P. Eberlein
Acknowledgements
The work was communicated when the first author was on deputation as Associate Professor, Department of Mathematics, Central University of Jammu, Sainik colony, Jammu-180011, India. The authors are thankful to the referees for their careful readings and helpful suggestions to improve the paper.
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