- International Electronic Journal of Geometry
- Vol: 16 Issue: 1
- Graph Surfaces Invariant by Parabolic screw Motions with Constant Curvature in $ \\: \\mathbb H^2 \\...
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 : 6 | Download : 2
Publication Date : 2023-04-30
Article Type : Research
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