University of Tabriz, Department of Pure Mathematics, Faculty of Mathematical Sci-
ences, Tabriz, Iran
Received March 9, 2016, revised December 15, 2016.
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.