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Bour’s Theorem of Spacelike Surfaces in Minkowski 4-Space

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Abstract

In this paper, we study on three kinds of spacelike helicoidal surfaces in Minkowski 4-space. First, we give an isometry between such helicoidal surfaces and rotational surfaces which is a kind of generalization of Bour’s theorem in Minkowski 3-space to Minkowski 4-space. Then, we show that if the isometric pair of surfaces have same Gauss map, then they are hyperplanar and minimal. Also, we give the parametrizations of isometric pair of surfaces having same Gauss map. Finally, we present some examples via Wolfram Mathematica 10.4.

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Acknowledgements

This work is a part of the master thesis of the third author and it is supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under Project 121F211.

Funding

This work is supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under Project 121F211.

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Author notes

  1. Murat Babaarslan and Yasin Küçükarıkan have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Yozgat Bozok University, 66100, Yozgat, Turkey

    Murat Babaarslan

  2. Department of Software Engineering, Fatih Sultan Mehmet Vakıf University, 34445, Istanbul, Turkey

    Burcu Bektaş Demirci

  3. Department of Mathematics, School of Graduates Studies, Yozgat Bozok University, 66100, Yozgat, Turkey

    Yasin Küçükarıkan

Authors
  1. Murat Babaarslan
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  2. Burcu Bektaş Demirci
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  3. Yasin Küçükarıkan
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MB, BBD and YK contributed to this work equally. MB, BBD and YK read and approved the final manuscript.

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Correspondence to Burcu Bektaş Demirci.

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Babaarslan, M., Bektaş Demirci, B. & Küçükarıkan, Y. Bour’s Theorem of Spacelike Surfaces in Minkowski 4-Space. Results Math 78, 12 (2023). https://doi.org/10.1007/s00025-022-01780-8

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