The Ruled Surfaces According to Type-2 Bishop Frame in the Euclidean 3-Space E^3

Abstract

We have introduced the ruled surfaces which are generated from the type-2 Bishop vectors. Then, we have calculated Gaussian curvatures, mean curvatures and integral invariants of these surfaces. Also the fundamental forms, geodesic curvatures, normal curvatures and geodesic torsions are calculated and some results are obtained.

Ruled Surfaces and Tangent Bundle of Unit 2-Sphere of Natural Lift Curves

“…The Gaussian curvature and mean curvature of ̅ are represented as: are taken for calculations, see [11].…”

“…A ruled surface is defined as the surface represented by moving a straight line in ℝ 3 , along a space curve defined as the base curve, see [4]. In the literature, there are a lot of studies about the properties of ruled surfaces, see [5][6][7][8][9][10][11][12]. W. K. Clifford pioneered the properties of dual numbers in 1873.…”