On the Cylinder Theorem in $M^2\times \mathbb{R}^n $

João L. M. Barbosa; G. Pacelli Bessa

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arXiv · 2203.02373

On the Cylinder Theorem in $M^2\times \mathbb{R}^n $

João L. M. Barbosa·G. Pacelli Bessa

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Abstract

Consider a surface $M^2$ with Gaussian curvature either $< 0$ or $> 0$. We prove that in $M^2\times \mathbb{R}^n$ cylinders are characterized as the hypersurfaces with both the extrinsic and intrinsic curvatures equal to zero.

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BibTeX RIS

João L. M. Barbosa, G. Pacelli Bessa. 2022-03-04. On the Cylinder Theorem in $M^2\times \mathbb{R}^n $. https://arxiv.org/abs/2203.02373

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