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

2024/04/15 by Kazan, Ahmet, Altın, Mustafa, Turgay, Nurettin Cenk
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.13075

Abstract

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 L_k 1-type Gauss map, first kind L_k-pointwise 1-type Gauss map, second kind L_k-pointwise 1-type Gauss map and L_k-harmonic Gauss map, k∈\1,2\.

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