Bulletin of the Korean Mathematical Society (대한수학회보)

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TIMELIKE TUBULAR SURFACES OF WEINGARTEN TYPES AND LINEAR WEINGARTEN TYPES IN MINKOWSKI 3-SPACE

  • Chenghong He (School of Mathematics and Statistics Nanjing University of Science and Technology) ;
  • He-jun Sun (School of Mathematics and Statistics Nanjing University of Science and Technology)
  • Received : 2023.03.05
  • Accepted : 2023.06.29
  • Published : 2024.03.31
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Abstract

Let K, H, KII and HII be the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature of a timelike tubular surface Tγ(α) with the radius γ along a timelike curve α(s) in Minkowski 3-space E31. We prove that Tγ(α) must be a (K, H)-Weingarten surface and a (K, H)-linear Weingarten surface. We also show that Tγ(α) is (X, Y)-Weingarten type if and only if its central curve is a circle or a helix, where (X, Y) ∈ {(K, KII), (K, HII), (H, KII), (H, HII), (KII , HII)}. Furthermore, we prove that there exist no timelike tubular surfaces of (X, Y)-linear Weingarten type, (X, Y, Z)-linear Weingarten type and (K, H, KII, HII)-linear Weingarten type along a timelike curve in E31, where (X, Y, Z) ∈ {(K, H, KII), (K, H, HII), (K, KII, HII), (H, KII, HII)}.

Keywords

Acknowledgement

This work was supported by the National Natural Science Foundation of China (Grant No. 11001130) and the Fundamental Research Funds for the Central Universities (Grant No. 30917011335).

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