Ruled Surfaces as Pseudospherical Congruences

Two-dimensional ruled surfaces in the spaces of constant curvature R n , S n , H n and in the Riemannian products S n × R 1 , H n × R 1 are considered. A ruled surface is proved to represent a pseudospherical congruence if and only if it is either an intrinsically flat surface in S n , or an intrinsically flat surface with constant extrinsic curvature in S n × R 1 .