Some remarks on the second variation formula for the area

Iff is a minimal, isometric immersion of the Riemannian manifoldM of dimensionn in a Riemannian manifold of dimensionm and ifI_N is the differential Jacobi operator acting on the cross sections of the normal bundleN(M), we obtain some information on the Morse index and on the stability ofM through a detailed geometric analysis of the immersionf obtained when considering the higher fundamental forms off.