We obtain the $\mathcal{L}_{1}$ (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 $\mathbb{E}^{4}_{1}$ and give some classifications for these hypersurfaces which have generalized $\mathcal{L}_{k}$ 1-type Gauss map, first kind $\mathcal{L}_{k}$-pointwise 1-type Gauss map, second kind $\mathcal{L}_{k}$-pointwise 1-type Gauss map and $\mathcal{L}_{k}$-harmonic Gauss map, $k\in\{1,2\}$.
📌 3 Key Takeaways
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Objective & Hypothesis:In this study, we deal with the Gauss map of tubular hypersurfaces in 4-dimensional Lorentz-Minkowski space concerning the linearized operators $\mathcal{L}_{1}$ (Cheng-Yau) and $\mathcal{L}_{2}$.
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Key Findings & Data:In this study, we deal with the Gauss map of tubular hypersurfaces in 4-dimensional Lorentz-Minkowski space concerning the linearized operators $\mathcal{L}_{1}$ (Cheng-Yau) and $\mathcal{L}_{2}$.
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Conclusion & Impact:We obtain the $\mathcal{L}_{1}$ (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 $\mathbb{E}^{4}_{1}$ and give some classifications for these hypersurfaces which have generalized $\mathcal{L}_{k}$ 1-type Gauss map, first kind $\mathcal{L}_{k}$-pointwise 1-type Gauss map, second kind $\mathcal{L}_{k}$-pointwise 1-type Gauss map and $\mathcal{L}_{k}$-harmonic Gauss map, $k\in\{1,2\}$.
In this study, we deal with the Gauss map of tubular hypersurfaces in 4-dimensional Lorentz-Minkowski space concerning the linearized operators $\mathcal{L}_{1}$ (Cheng-Yau) and $\mathcal{L}_{2}$. We obtain the $\mathcal{L}_{1}$ (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 $\mathbb{E}^{4}_{1}$ and give some classifications for these hypersurfaces which have generalized $\mathcal{L}_{k}$ 1-type Gauss map, first kind $\mathcal{L}_{k}$-pointwise 1-type Gauss map, second kind $\mathcal{L}_{k}$-pointwise 1-type Gauss map and $\mathcal{L}_{k}$-harmonic Gauss map, $k\in\{1,2\}$.
Kazan, A., Altın, M., Turgay, N. C. (2025). Some classifications for Gauss map of Tubular hypersurfaces in $\mathbb{E}^{4}_{1}$ concerning linearized operators $\mathcal{L}_{k}$. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 4. https://doi.org/10.15672/hujms.1468581
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