Parallel and semi-parallel immersions into space forms
Received: 25 June 1992
Mathematics Subject Classification: 53C42
Abstract The geometry of a submanifold of a space form is described by the second fundamental form. Therefore it is natural to study isometric immersions whose second fundamental form are simple in some sense. In this paper we will describe some (by now classical) results on parallel immersions, i.e. immersions whose second fundamental form is covariantly constant, and some more recent results on semi-parallel immersions, i.e. immersions whose second fundamental form verifies the corresponding integrability condition. It is probably worthwhile to observe that the above condition are the analog, in submanfolds theory, of what symmetric and semi-symmetric spaces are in intrinsic riemannian geometry.