Skewable matrices over $\wedge^2 V$ applied to locally metric connections

Abstract

A necessary condition for a connection in a vector bundle to be locally metric is for its curvature matrix, which consists of $2$ forms, to be skew symmetric with respect to some local frame. In this paper we give a simple algorithm that can be used to decide when a matrix of $2$ forms is equivalent to a skew symmetric matrix. We apply this algorithm to verify whether a "{\it full rank}" curvature connection is locally metric.