  We study the geometry of jets of submanifolds with special interest in the
relationship with the calculus of variations. We give a new proof of the fact
that higher order jets of submanifolds are affine bundles; as a by-product we
obtain a new expression for the associated vector bundles. We use
Green-Vinogradov formula to provide coordinate expressions for all variational
forms, i.e., objects in the finite-order variational sequence on jets of
submanifolds. Finally, we formulate the variational problem in the framework of
jets of submanifolds by an intrinsic geometric language, and connect it with
the variational sequence. Detailed comparison with literature is provided
throughout the paper.
