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$L_k$-Biharmonic hypersurfaces in the 3-or 4-dimensional Lorentz-Minkowski spaces | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 187-200 اصل مقاله (525.28 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19592.1272 | ||
| نویسندگان | ||
| Rahim Hoseinoghli؛ Akram Mohammadpouri* | ||
| Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran | ||
| چکیده | ||
| A hypersurface $ M^n $ in the Lorentz-Minkowski space $\mathbb{L}^{n+1} $ is called $ L_k $-biharmonic if the position vector $ \psi $ satisfies the condition $ L_k^2\psi =0$, where $ L_k$ is the linearized operator of the $(k+1)$-th mean curvature of $ M $ for a fixed $k=0,1,\ldots,n-1$. This definition is a natural generalization of the concept of a biharmonic hypersurface. We prove that any $ L_k $-biharmonic surface in $ \mathbb{L}^3 $ is $k$-maximal. We also prove that any $ L_k $-biharmonic hypersurface in $ \mathbb{L}^4 $ with constant $ k$-th mean curvature is $ k $-maximal. These results give a partial answer to the Chen's conjecture for $L_k$-operator that $L_k$-biharmonicity implies $L_k$-maximality. | ||
| کلیدواژه‌ها | ||
| Linearized operator $L_k$؛ $L_k$-biharmonic hypersurface؛ $k$-maximal hypersurface؛ $k$-th mean curvature | ||
| مراجع | ||
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