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arXiv · 1812.08676

Rotational Surfaces with second fundamental form of constant length

Alexandre P. Barreto·Francisco Fontenele·Luiz Hartmann
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Abstract

We obtain an infinite family of complete non embedded rotational surfaces in $\mathbb R^3$ whose second fundamental forms have length equal to one at any point. Also we prove that a complete rotational surface with second fundamental form of constant length is either a round sphere, a circular cylinder or, up to a homothety and a rigid motion, a member of that family. In particular, the round sphere and the circular cylinder are the only complete embedded rotational surfaces in $\mathbb R^3$ with second fundamental form of constant length.

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Alexandre P. Barreto, Francisco Fontenele, Luiz Hartmann. 2018-12-20. Rotational Surfaces with second fundamental form of constant length. https://arxiv.org/abs/1812.08676

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