Pseudo-parallel surfaces of S c n × R and H c n × R

In this work we give a characterization of pseudo-parallel surfaces in Scn×R and Hcn×R, extending an analogous result by Asperti-Lobos-Mercuri for the pseudo-parallel case in space forms. Moreover, when n=3, we prove that any pseudo-parallel surface has flat normal bundle. We also give examples of pseudo-parallel surfaces which are neither semi-parallel nor pseudo-parallel surfaces in a slice. Finally, when n≥4 we give examples of pseudo-parallel surfaces with non vanishing normal curvature.