An approach for designing a surface pencil through a given geodesic   curve
  Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface interpolating a given curve as the geodesic curve of it. Also, we analyze the conditions when the resulting surface is a ruled surface. In addition, developablity along the common geodesic of the members of surface family are discussed. Finally, we illustrate this method by presenting some examples. 
Gulnur Saffak Atalay, Fatma Guler, Ergin Bayram and Emin Kasap
math.DG