Deltohelicoidal surfaces

Abstract

The surface theory has been working by many mathematicians, and also geometers for hundreds of years. We meet nice papers and books for the theory in the literature. In this paper, we consider deltohelicoidal surface in Euclidean 3-space E^3. We show some basic notions of three dimensional Euclidean geometry. Moreover, constructing a helicoidal surface, we define deltohelicoidal surface, and compute its Gauss map, the Gaussian curvature and the mean curvature. Finally, we reveal some results of the Gaussian curvature and the mean curvature of the deltohelicoidal surface in the three dimensional Euclidean space E^3.