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

Authors : Uğur DURSUN

Pages : 215-224

Doi:10.36890/iejg.1231759

View : 55 | Download : 7

Publication Date : 2023-04-30

Article Type : Research Paper

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, extrinsic curvature

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