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

Document Type : Research Paper


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


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.


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Volume 10, Issue 1
May 2021
Pages 69-78
  • Receive Date: 14 April 2020
  • Revise Date: 07 March 2021
  • Accept Date: 15 April 2021
  • First Publish Date: 01 May 2021