Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density

Abstract

In this paper, we obtain the weighted mean and weighted Gaussian curvatures of surfaces of revolution in Galilean 3-space with density $e^{a_{1}x^{2}+a_{2}y^{2}+a_{3}z^{2}}$, $a_{1},a_{2},a_{3} \in R$ not all zero. Also, we investigate some cases of weighted minimal surfaces of revolution according to $a_{i},$ $i=1,2,3$ and weighted flat surfaces of revolution.