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This article is cited in 3 scientific papers (total in 3 papers)
Hypersurfaces with $L_r$-pointwise $1$-type Gauss map
Akram Mohammadpouri University of Tabriz, Department of Pure Mathematics, Faculty of Mathematical Sciences, Tabriz, Iran
Abstract:
In this paper, we study hypersurfaces in $\mathbb E^{n+1}$ whose Gauss map $G$ satisfies the equation $L_rG = f(G + C)$ for a smooth function $f$ and a constant vector $C$, where $L_r$ is the linearized operator of the $(r + 1)$-st mean curvature of the hypersurface, i.e., $L_r(f)=\mathop{\mathrm{Tr}}(P_r\circ\nabla^2f)$ for $f\in \mathcal{C}^\infty(M)$, where $P_r$ is the $r$-th Newton transformation, $\nabla^2f$ is the Hessian of $f$, $L_rG=(L_rG_1,\ldots,L_rG_{n+1})$ and $G=(G_1,\ldots,G_{n+1})$. We focus on hypersurfaces with constant $(r+1)$-st mean curvature and constant mean curvature. We obtain some classification and characterization theorems for these classes of hypersurfaces.
Key words and phrases:
linearized operators $L_r$, $L_r$-pointwise $1$-type Gauss map, $r$-minimal hypersurface.
Received: 09.03.2016 Revised: 15.12.2016
Citation:
Akram Mohammadpouri, “Hypersurfaces with $L_r$-pointwise $1$-type Gauss map”, Zh. Mat. Fiz. Anal. Geom., 14:1 (2018), 67–77
Linking options:
https://www.mathnet.ru/eng/jmag689 https://www.mathnet.ru/eng/jmag/v14/i1/p67
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Abstract page: | 103 | Full-text PDF : | 44 | References: | 18 |
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