English

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

Differential Geometry 2016-07-20 v1

Abstract

A necessary condition for a connection in a vector bundle to be locally metric is for its curvature matrix, which consists of 22 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 22 forms is equivalent to a skew symmetric matrix. We apply this algorithm to verify whether a "{\it full rank}" curvature connection is locally metric.

Keywords

Cite

@article{arxiv.1607.05662,
  title  = {Skewable matrices over $\wedge^2 V$ applied to locally metric connections},
  author = {Mihail Cocos and Kent Kidman},
  journal= {arXiv preprint arXiv:1607.05662},
  year   = {2016}
}