# Proper Lk-biharmonic Hypersurfaces in The Euclidean Sphere with Two Principal Curvatures

Document Type : Research Paper

Authors

Dept. of Math, Rafsanjan University of Vali-e-Asr, Iran

Abstract

In this paper we classify proper $L_k$-biharmonic hypersurfaces $M$, in the unit Euclidean sphere which has two principal curvatures and we show that they are open pieces of standard products of spheres. Also we study proper $L_k$-biharmonic compact hypersurfaces $M$ with respect to $tr(S^2\circ P_k)$ and $H_k$ where $S$ is the shape operator, $P_k$ is the Newton transformation and $H_k$ is the $k$-th mean curvature of $M$, and by definiteness's assumption of $P_k$, we show that $H_{k+1}$ is constant.

Keywords

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### History

• Receive Date: 14 April 2020
• Revise Date: 07 March 2021
• Accept Date: 15 April 2021
• First Publish Date: 01 May 2021