Ruled surfaces with null curves and Frenet frame in pseudo-sphere and pseudo-hyperbolic space

Abstract

In this paper, we construct Frenet frame fields along a null curve when it is not a bi-null Cartan curve in a pseudo-hyperbolic space with index 2 and pseudo-sphere with index 2, respectively. Also, we find ruled surfaces with the above null curves which have non-diagonalizable shape operators, constant mean curvatures and constant scalar curvatures.