Pseudo-Parallel submanifolds

Pseudo-parallel (shortly PP) submanifolds are defined as a generalization of semi-parallel (shortly SP ) submanifolds and as extrinsic analogue of pseudo-symmetric (shortly PS) manifolds (in the sense of R. Deszcz) [1], [26]. Asperti et al [1] obtained a description of PP hypersurfaces in space form as quasiumbilic hypersurfaces or cyclids of Dupin and studied PP surfaces with maximal first normal bundle in space form and classified complete simply connected PP submanifolds in space. In the last years many results obtained about a class of surfaces in Euclidean space, pseudo-parallel hypersurfaces in pseudo-Riemannian space forms and pseudo-parallel real hypersurfaces in complex space forms, appeared in [19], [15], [16] respectively. In this paper we study the PP hypersurfaces in Riemannian manifold not necessarily a space form; Moreover we give a description of semi-parallel surfaces in BCV spaces. Mathematics Subject classification: 53C40 53C35.