A GEOMETRIC LAGRANGIAN FORMALISM FOR EXTENDED OBJECTS D. R. Grigore Abstract. A geometric generalization of the first-order Lagrangian formalism is used to analyse extended objects (i.e. $p$-branes). We show that the condition that reparametrizations and Galilei transformations are Noetherian symmetries, lead uniquely to a Lagrangian which is a sum of two contributions: a ``Nambu-Goto'' term (which appears only for particles i.e. $p = 1$) and a ``Chern-Simons''-like contribution. Keywords. Lagrangian Formalism, Noether theorem, Extended Objects. MS classification. 53A30, 58G25.