Smarandache ruled surfaces with modified orthogonal frame in R^3

Abstract

This article introduces a new approach for constructing ruled surfaces in Euclidean 3-space, particularly TN, TB and NB Smarandache ruled surfaces. We investigate their Gaussian and mean curvatures to classify them as developable and minimal surfaces. Additionally, we study the geodesic and normal curvatures associated with the base curve of each ruled surface. Moreover, some conditions are derived under which the base curve is a geodesic or an asymptotic line. The striction curve corresponding to each ruled surface is also computed. Finally, we give some examples with their graphical representations.