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arXiv · math-ph/0212048

Metric Tensor Vs. Metric Extensor

V. V. Fernández·A. M. Moya·Waldyr A. Rodrigues Jr
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Abstract

In this paper we give a comparison between the formulation of the concept of metric for a real vector space of finite dimension in terms of \emph{tensors} and \emph{extensors}. A nice property of metric extensors is that they have inverses which are also themselves metric extensors. This property is not shared by metric tensors because tensors do \emph{not} have inverses. We relate the definition of determinant of a metric extensor with the classical determinant of the corresponding matrix associated to the metric tensor in a given vector basis. Previous identifications of these concepts are equivocated. The use of metric extensor permits sophisticated calculations without the introduction of matrix representations.

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V. V. Fernández, A. M. Moya, Waldyr A. Rodrigues Jr. 2002-12-16. Metric Tensor Vs. Metric Extensor. https://arxiv.org/abs/math-ph/0212048

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