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Complete Space-like λ-surfaces in the Minkowski Space \(ℝ_1^3\) with the Second Fundamental Form of Constant Length

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Abstract

In this paper we study the complete space-like λ-surfaces in the three dimensional Minkowski space \(ℝ_1^3\). As the result, we obtain a complete classification theorem for all the complete space-like λ-surfaces \(x:{M^2} \to ℝ_1^3\) with the second fundamental form of constant length. This is a natural extension to the λ-surfaces in \(ℝ_1^3\) of a recent interesting classification theorem by Cheng and Wei for λ-surfaces in the Euclidean space ℝ3.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Henan Normal University Xinxiang, Xinxiang, 453007, P. R. China

    Xing Xiao Li, Yang Yang Liu & Rui Na Qiao

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  1. Xing Xiao Li
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  2. Yang Yang Liu
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  3. Rui Na Qiao
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Correspondence to Xing Xiao Li.

Additional information

Supported by Natural Science Foundation of China (Grant Nos. 11671121, 11871197 and 11971153)

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Li, X.X., Liu, Y.Y. & Qiao, R.N. Complete Space-like λ-surfaces in the Minkowski Space \(ℝ_1^3\) with the Second Fundamental Form of Constant Length. Acta. Math. Sin.-English Ser. 36, 559–577 (2020). https://doi.org/10.1007/s10114-020-9078-x

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  • DOI: https://doi.org/10.1007/s10114-020-9078-x

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