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Universal Journal of Applied Mathematics Vol. 5(5), pp. 106 - 113
DOI: 10.13189/ujam.2017.050503
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Skewable Matrices over ∧²V Applied to Locally Metric Connections

Mihail Cocos , Kent Kidman ^*
Department of Mathematics, Weber State University, USA

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 full rank curvature connection is locally metric.

KEYWORDS
Simultaneously Skew Matrices, Linear Connections, Metric Compatible Connections, Full Rank Curvature

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mihail Cocos , Kent Kidman , "Skewable Matrices over ∧²V Applied to Locally Metric Connections," Universal Journal of Applied Mathematics, Vol. 5, No. 5, pp. 106 - 113, 2017. DOI: 10.13189/ujam.2017.050503.

(b). APA Format:
Mihail Cocos , Kent Kidman (2017). Skewable Matrices over ∧²V Applied to Locally Metric Connections. Universal Journal of Applied Mathematics, 5(5), 106 - 113. DOI: 10.13189/ujam.2017.050503.