Applied Mathematical Sciences, Vol. 14, 2020, no. 4, 171 - 183 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2020.912175 Gaussian Curvatures of Parallel Ruled Surfaces S¨ uleyman S ¸enyurt Faculty of Arts and Sciences, Department of Mathematics Ordu University Ordu, Turkey S¨ umeyye G¨ ur Mazlum Department of Computer Technology G¨ um¨ u¸ shane University, G¨ um¨ u¸ shane, Turkey Luca Grilli 1 Department of Economics, University of Foggia, Foggia, Italy This article is distributed under the Creative Commons by-nc-nd Attribution License. Copyright c  2020 Hikari Ltd. Abstract In this paper, the Gaussian curvatures of closed parallel ruled sur- faces are calculated. We consider parallel ruled surfaces from indicatrix curves associated to Frenet vectors of the curve created on the unit dual sphere. Mathematics Subject Classification: 53A04, 53A05, 53A17 Keywords: Parallel Surfaces; Gaussian Curvature, Dual Ruled Surfaces 1 Introduction The Frenet vectors given by the length parameter of a curve on unit dual sphere can be found with classical methods. It is well known that if these curves move at the center of the unit dual sphere, they generate indicatrix 1 Corresponding author