2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71939We review the notions of symplectic and orthogonal vector bundles over curves, and the connection between principal parts and extensions of vector bundles. We give a criterion for a certain extension of rank 2n to be symplectic or orthogonal. We then describe almost all of its rank n vector subbundles using graphs of sheaf homomorphisms, and give criteria for the isotropy of these subbundles.13 pages; refinement of main result addedAlgebraic Geometry14H60text