Journal of Mathematical Physics, Analysis, Geometry
2018, vol. 14, No 1, pp. 67-77   https://doi.org/10.15407/mag14.01.067     ( to contents , go back )
https://doi.org/10.15407/mag14.01.067

Hypersurfaces with Lr-Pointwise 1-Type Gauss Map

Akram Mohammadpouri

University of Tabriz, Department of Pure Mathematics, Faculty of Mathematical Sci- ences, Tabriz, Iran
E-mail: pouri@tabrizu.ac.ir

Received March 9, 2016, revised December 15, 2016.

Abstract

In this paper, we study hypersurfaces in 𝔼n+1 whose Gauss map G satisfies the equation LrG = f(G + C) for a smooth function f and a constant vector C, where Lr is the linearized operator of the (r+1)-st mean curvature of the hypersurface, i.e., Lr(f) = Tr(Pr ○∇2f) for f ∈ 𝐶(M), where Pr is the r-th Newton transformation, ∇2f is the Hessian of f, LrG = (LrG1, . . . ,LrGn+1) and G = (G1, . . . ,Gn+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.

Mathematics Subject Classification 2000: 53D02, 53C40, 53C42
Key words: linearized operators Lr, Lr-pointwise 1-type Gauss map, r-minimal hypersurface.

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