ON SURFACES WITH COMMON PSEUDO NULL GEODESIC IN MINKOWSKI 3-SPACE

Abstract

The problem of constructing a family of parametric surfaces froma given pseudo null curve using the Frenet trihedron frame of the curve in theMinkowski 3-space is studied. The necessary and su¢ cient conditions for thegiven pseudo null curve to be a common geodesic of the parametric surface arederived. As a member of the family, considered a ruled surface with a pseudonull directrix, and some corollaries on the ruled surface are given. Also, someexamples are given to show the family of surfaces with a common pseudo null geodesic.