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Proper Lk-biharmonic Hypersurfaces in The Euclidean Sphere with Two Principal Curvatures | ||
Journal of Mahani Mathematical Research | ||
دوره 10، شماره 1، مرداد 2021، صفحه 69-78 اصل مقاله (476.92 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.15736.1116 | ||
نویسندگان | ||
Mehran Aminian* ؛ Mehran Namjoo | ||
Dept. of Math, Rafsanjan University of Vali-e-Asr, Iran | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
L_k operator؛ biharmonic hypersurfaces؛ Chen conjecture | ||
مراجع | ||
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