Graph Surfaces Invariant by Parabolic screw Motions with Constant Curvature in $ \: \mathbb H^2 \times \mathbb R$

Year 2023, Volume: 16 Issue: 1, 215 - 224, 30.04.2023

Uğur Dursun

https://doi.org/10.36890/iejg.1231759

Abstract

In this work we study vertical graph surfaces invariant by parabolic screw motions with pitch $\ell >0$ and constant Gaussian curvature or constant extrinsic curvature in the product space $\mathbb H^2 \times \mathbb R$. In particular, we determine flat and extrinsically flat graph surfaces in $\mathbb H^2 \times \mathbb R$. We also obtain complete and non-complete vertical graph surfaces in $\mathbb H^2 \times \mathbb R$ with negative constant Gaussian curvature and zero extrinsic curvature.

Keywords

Parabolic screw motion, graph surface, Gauss curvature, extrinsic curvature, flat surface

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