Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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BICONSERVATIVE PNMCV SURFACES IN THE ARBITRARY DIMENSIONAL MINKOWSKI SPACE

  • Nurettin Cenk Turgay (Faculty of Science and Letters Department of Mathematics Istanbul Technical University) ;
  • Ruya Yegin Sen (Faculty of Engineering and Natural Sciences Department of Mathematics Istanbul Medeniyet University)
  • Received : 2023.11.28
  • Accepted : 2024.06.11
  • Published : 2025.01.01
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Abstract

In this article, we study biconservative surfaces with parallel normalized mean curvature vector field in the arbitrary dimensional Minkowski space 𝔼m1, where m ≥ 4. Firstly, we obtain some geometric properties of these surfaces. In particular, we prove that if M is a PNMCV biconservative surface in 𝔼m1, then it must be contained in a 4-dimensional non-degenerated totally geodesic of 𝔼m1 and all its shape operators are diagonalizable. Then, we give local classification theorems for biconservative PNMCV space-like and time-like surfaces in 𝔼41.

Keywords

Acknowledgement

This work was carried out during a 3501 project supported by the Scientific and Technological Research Council of Turkiye (TUBITAK), Project Number:121F253.

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