Metric Compatible Covariant Derivatives

W. A. Rodrigues Jr.; V. V. Fernandez; A. M. Moya

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Metric Compatible Covariant Derivatives

W. A. Rodrigues Jr.·V. V. Fernandez·A. M. Moya

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Abstract

This paper, sixth in a series of eight, uses the geometric calculus on manifolds developed in previous papers of the series to introduce through the concept of a metric extensor field g a metric structure for a smooth manifold M. The associated Christoffel operators, a notable decomposition of that object and the associated Levi-Civita connection field are given. The paper introduces also the concept of a geometrical structure for a manifold M as a triple (M,g,gamma), where gamma is a connection extensor field defining a parallelism structure for M . Next, the theory of metric compatible covariant derivatives is given and a relationship between the connection extensor fields and covariant derivatives of two deformed (metric compatible) geometrical structures (M,g,gamma) and (M,eta,gamma') is determined.

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BibTeX RIS

W. A. Rodrigues Jr., V. V. Fernandez, A. M. Moya. 2006-08-30. Metric Compatible Covariant Derivatives. https://arxiv.org/abs/math/0501561

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