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Hypersurfaces with Non-diagonalizable Shape Operators in Minkowski Spaces

  • Zülal Derin Yaqub
  • Nurettin Cenk Turgay
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Abstract

In this paper, we study hypersurfaces M4 in the Minkowski space 𝔼51 whose shape operator S is non-diagonalizable, having a triple real eigenvalue λ with a one-dimensional eigenspace together with a simple eigenvalue μ (Case~(iii) in the classification of Magid). Assuming that λ and μ satisfy a functional relation λ=f(μ) and that the eigenvector field of μ is geodesic, we show that λ and μ, as well as the pseudo-orthonormal frame, are intrinsic invariants of M, determined by the induced metric up to sign. As a consequence, we prove that such hypersurfaces are unique up to isometries of 𝔼51. We also obtain a classification of the warped product hypersurfaces of this type.

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Cite

BibTeXRIS
BibTeX
@misc{yaqub2026hypersurfaces,
  title = {{Hypersurfaces with Non-diagonalizable Shape Operators in Minkowski Spaces}},
  author = {Zülal Derin Yaqub and Nurettin Cenk Turgay},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18896},
  eprint = {2610.18896},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18896},
}
RIS
TY  - UNPB
TI  - Hypersurfaces with Non-diagonalizable Shape Operators in Minkowski Spaces
AU  - Zülal Derin Yaqub
AU  - Nurettin Cenk Turgay
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.18896
UR  - https://arxiv.org/abs/2610.18896
AB  - In this paper, we study hypersurfaces M^4 in the Minkowski space 𝔼^5_1 whose shape operator S is non-diagonalizable, having a triple real eigenvalue λ with a one-dimensional eigenspace together with a simple eigenvalue μ (Case~(iii) in the classification of Magid). Assuming that λ and μ satisfy a functional relation λ=f(μ) and that the eigenvector field of μ is geodesic, we show that λ and μ, as well as the pseudo-orthonormal frame, are intrinsic invariants of M, determined by the induced metric up to sign. As a consequence, we prove that such hypersurfaces are unique up to isometries of 𝔼^5_1. We also obtain a classification of the warped product hypersurfaces of this type.
ER  -