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arXiv · 2511.08557

On Laguerre Isotropic Hypersurfaces

Fernanda Alves Caixeta·Keti Tenenblat
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Abstract

We study Laguerre isotropic hypersurfaces in the Euclidean space, which are hypersurfaces whose Laguerre form is zero and the eigenvalues of the Laguerre tensor are constant and equal to $\lambda\geq 0$. We prove a rigidity theorem for the L-isotropic hypersurfaces parametrized by lines of curvature. Moreover, we study the hypersurfaces that are L-isotropic and L-isoparametric simultaneously and we show that for such a hypersurface $\lambda=0$. We obtain necessary conditions for the existence of L-isotropic hypersurfaces with $\lambda > 0$ and we prove that a certain function, determined by the radii of curvature of the hypersurface, is bounded above by ${1}/{2\lambda}$.

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Fernanda Alves Caixeta, Keti Tenenblat. 2025-11-11. On Laguerre Isotropic Hypersurfaces. https://arxiv.org/abs/2511.08557

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