Hypersurface family with a common isoasymptotic curve
  In the present paper, we handle the problem of finding a hypersurface family from a given asymptotic curve in R^4. Using the Frenet frame of the given asymptotic curve, we express the hypersurface as a linear combination of this frame and analyze the necessary and sufficient conditions for that curve to be asymptotic. We illustrate this method by presenting some examples. 
Ergin Bayram, Emin Kasap
math.DG