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Biconservative surfaces with constant mean curvature in lorentzian space forms

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Abstract

In this paper, we consider biconservative and biharmonic isometric immersions into the 4-dimensional Lorentzian space form \({\mathbb {L}}^4(\delta )\) with constant sectional curvature \(\delta \). We obtain some local classifications of biconservative CMC surfaces in \({\mathbb {L}}^4(\delta )\). Further, we get complete classification of biharmonic CMC surfaces in the de Sitter 4-space. We also proved that there is no biharmonic CMC surface in the anti-de Sitter 4-space. Further, we get the classification of biconservative, quasi-minimal surfaces in Minkowski-4 space.

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Acknowledgements

This work is a part of the first author’s doctoral thesis. The manuscript has no associate data.

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Authors and Affiliations

  1. Maltepe University, Maltepe, Istanbul, Turkey

    Aykut Kayhan

  2. Faculty of Science and Letters, Department of Mathematics, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey

    Nurettin Cenk Turgay

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  1. Aykut Kayhan
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  2. Nurettin Cenk Turgay
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Correspondence to Nurettin Cenk Turgay.

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Communicated by Vicente Cortés.

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Kayhan, A., Turgay, N.C. Biconservative surfaces with constant mean curvature in lorentzian space forms. Abh. Math. Semin. Univ. Hambg. (2024). https://doi.org/10.1007/s12188-023-00273-x

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  • DOI: https://doi.org/10.1007/s12188-023-00273-x

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