The Invariants of Dual Parallel Equidistant Ruled Surfaces
Sümeyye GÜR MAZLUM, Süleyman Şenyurt, Luca Grilli
Abstract
In this paper, we calculate the Gaussian curvatures of the dual spherical indicatrix curves formed on unit dual sphere by the Blaschke vectors and dual instantaneous Pfaff vectors of dual parallel equidistant ruled surfaces (DPERS) and we give the relationships between these curvatures. In addition to—in cases where the base curves of these DPERS are closed—computing the dual integral invariants of the indicatrix curves. Additionally, we show the relationships between them. Finally, we provide an example for each of these indicatrix curves.
Topics & Concepts
EquidistantDual (grammatical number)MathematicsRuled surfaceUnit (ring theory)Gaussian curvatureBase (topology)Mathematical analysisGaussianGeometryPure mathematicsSurface (topology)CurvaturePhysicsQuantum mechanicsArtMathematics educationLiterature3D Shape Modeling and AnalysisAdvanced Numerical Analysis TechniquesGeometric Analysis and Curvature Flows