23\(^{\text{o}}\) colóquio Brasileiro de matemática (Q2754858)

The first part of these lecture notes contains an exposition of some basic facts of Riemannian geometry (including Ambrose-Singer theorem and Berger's classification of the holonomy groups of Riemannian manifolds) and geometry of submanifolds . The second part deals with submanifolds \(M\) of the Euclidean space \(E^N\). The author's classification of possible holonomy groups of the normal connection of \(M\) is presented and a proof is indicated. Application of this classification to many interesting classes of submanifolds (totally umbilical submanifolds, submanifolds with flat normal bundle, parallel submanifolds, submanifolds with constant principal curvatures, isoparametric submanifolds, holonomy tubes) is given.