Some Classifications for Gauss Map of Tubular Hypersurfaces in E⁴₁ Concerning Linearized Operators Lₖ

In this study, we deal with the Gauss map of tubular hypersurfaces in 4-dimensional Lorentz-Minkowski space concerning the linearized operators L₁ (Cheng-Yau) and L₂. We obtain the L₁ (Cheng-Yau) operator of the Gauss map of tubular hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres {or pseudo hyperbolic hyperspheres} whose centers lie on timelike or spacelike curves with non-null Frenet vectors in E⁴₁ and give some classifications for these hypersurfaces which have generalized Lₖ 1-type Gauss map, first kind Lₖ-pointwise 1-type Gauss map, second kind Lₖ-pointwise 1-type Gauss map and Lₖ-harmonic Gauss map, k∈\1,2\.