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arXiv · 2610.18896

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 $M^4$ in the Minkowski space $\mathbb{E}^5_1$ 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 $\mathbb{E}^5_1$. We also obtain a classification of the warped product hypersurfaces of this type.

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Zülal Derin Yaqub, Nurettin Cenk Turgay. 2026-10-10. Hypersurfaces with Non-diagonalizable Shape Operators in Minkowski Spaces. https://arxiv.org/abs/2610.18896

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