AUTHOR=Mosa Safaa , Elzawy Mervat 

TITLE=Helicoidal Surfaces in Galilean Space With Density

JOURNAL=Frontiers in Physics

VOLUME=8

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00081

DOI=10.3389/fphy.2020.00081

ISSN=2296-424X

ABSTRACT=<p>In this paper, we construct helicoidal surfaces in the three dimensional Galilean space <italic>G</italic><sup>3</sup>. The First and the Second Fundamental Forms for such surfaces will be obtained. Also, mean and Gaussian curvature given by smooth functions will be derived. We consider the Galilean 3−space with a linear density <italic>e</italic><sup>ϕ</sup> and construct a weighted helicoidal surfaces in <italic>G</italic><sup>3</sup> by solving a second order non-linear differential equation. Moreover, we discuss the problem of finding explicit parameterization for the helicoidal surfaces in <italic>G</italic><sup>3</sup>.</p><p>M.S.C.2010: 53<italic>A</italic>35, 51<italic>A</italic>05</p>