Biconservative surfaces with constant mean curvature in Lorentzian space forms

Aykut Kayhan; Nurettin Cenk Turgay

doi:10.1007/s12188-023-00273-x

Biconservative surfaces with constant mean curvature in Lorentzian space forms

Aykut Kayhan, Nurettin Cenk Turgay^*

^*Corresponding author for this work

Department of Mathematics Engineering

Maltepe University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider biconservative and biharmonic isometric immersions into the 4-dimensional Lorentzian space form L⁴(δ) with constant sectional curvature δ. We obtain some local classifications of biconservative CMC surfaces in L⁴(δ). 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.

Original language	English
Pages (from-to)	19-31
Number of pages	13
Journal	Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume	94
Issue number	1
DOIs	https://doi.org/10.1007/s12188-023-00273-x
Publication status	Published - Apr 2024

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Mathematisches Seminar der Universität Hamburg 2024.

Keywords

Biconservative surfaces
Constant mean curvature
Lorentzian space forms
Quasi-minimal surfaces
de Sitter space

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10.1007/s12188-023-00273-x

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AB - In this paper, we consider biconservative and biharmonic isometric immersions into the 4-dimensional Lorentzian space form L4(δ) with constant sectional curvature δ. We obtain some local classifications of biconservative CMC surfaces in L4(δ). 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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KW - Lorentzian space forms

KW - Quasi-minimal surfaces

KW - de Sitter space

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Biconservative surfaces with constant mean curvature in Lorentzian space forms

Abstract

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Keywords

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