Skewable matrices over \wedge² V applied to locally metric connections

2016/07/18 by Cocos, Mihail, Kidman, Kent
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.05662

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.

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