Evolution of space curves and the special ruled surfaces with modified orthogonal frame
Kemal Eren, Hidayet Hüda Kösal
Abstract
In this study, we investigate the evolution of space curves and the special ruled surfaces with modified orthogonal frame. Firstly, we recall the relations between the Serret-Frenet frame and the modified orthogonal frame. Then we investigate the evolution of space curves relative to these relations. Moreover, we determine the first and second fundamental forms, the Gaussian and mean curvatures of the tangent, normal, and binormal ruled surfaces according to the modified frame. In these regards, we obtain the characterizations of the minimal and developable ruled surfaces based on modified orthogonal frame.
Topics & Concepts
Frenet–Serret formulasMathematicsRuled surfaceFrame (networking)TangentSpace frameSpace (punctuation)GaussianPure mathematicsMathematical analysisGeometrySurface (topology)PhysicsComputer scienceCurvatureThermodynamicsOperating systemTelecommunicationsQuantum mechanicsGeometric Analysis and Curvature FlowsAdvanced Numerical Analysis TechniquesNonlinear Waves and Solitons