Emin Kasap

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We investigate minimal surfaces passing a given curve in R3. Using the Frenet frame of a given curve and isothermal parameter, we derive the necessary and sufficient condition for minimal surface. Also we derive the parametric representation of two minimal surface families passing a circle and a helix as Examples Mathematics Subject Classification: 53A10,(More)
A non-linear differential equation is analyzed to determine the geodesic curves on ruled surfaces with time-like rulings inR31. When it is assumed that curvature and torsion of the base curve and components with respect to Frenet’s frame of time-like straight-line are constants, for a special integration constant, it appears that the resulting non-linear(More)
A curve which is called geodesic on a surface M in Lorentz 3-space is a special curve that its acceleration is everywhere normal to M. In this paper, we analyzed the non-linear differential equation to determine the geodesic curves on ruled surfaces which is obtained by a strictly connected spacelike straight line moving with Frenet’s frame along a timelike(More)