  We study the relation between various notions of exterior convexity
introduced in Bandyopadhyay-Dacorogna-Sil \cite{BDS1} with the classical
notions of rank one convexity, quasiconvexity and polyconvexity. To this end,
we introduce a projection map, which generalizes the alternating projection for
two-tensors in a new way and study the algebraic properties of this map. We
conclude with a few simple consequences of this relation which yields new
proofs for some of the results discussed in Bandyopadhyay-Dacorogna-Sil
\cite{BDS1}.
