TY - JOUR ID - 2895 TI - Proper Lk-biharmonic Hypersurfaces in The Euclidean Sphere with Two Principal Curvatures JO - Journal of Mahani Mathematical Research JA - JMMR LA - en SN - 2251-7952 AU - Aminian, Mehran AU - Namjoo, Mehran AD - Dept. of Math, Rafsanjan University of Vali-e-Asr, Iran Y1 - 2021 PY - 2021 VL - 10 IS - 1 SP - 69 EP - 78 KW - L_k operator KW - biharmonic hypersurfaces KW - Chen conjecture DO - 10.22103/jmmrc.2021.15736.1116 N2 - 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. UR - https://jmmrc.uk.ac.ir/article_2895.html L1 - https://jmmrc.uk.ac.ir/article_2895_2e22507b06578ffe35eed4537696faec.pdf ER -