Nonlinear connections for conformal gauge theories on path-spaces and duality (Q2915427)
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scientific article; zbMATH DE number 6083259
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear connections for conformal gauge theories on path-spaces and duality |
scientific article; zbMATH DE number 6083259 |
Statements
Nonlinear connections for conformal gauge theories on path-spaces and duality (English)
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17 September 2012
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semispray
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conformal class of metrics
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Weyl structure
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compatible non-linear connection
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conformal path-gauge invariance
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duality for nonlinear connections
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Weyl structures and compatible nonlinear connections are introduced in the geometry of semisprays as a natural generalization of similar notions from Riemannian geometry. The existence and formula for the set of all compatible nonlinear connections are derived by using the Obata tensors naturally associated to a fixed metric in the given conformal class; this formula is also expressed in terms of dual nonlinear connections which generalize the Norden's notion of dual linear connections. A geometric meaning for pairs (Weyl structure, compatible nonlinear connection) is provided in terms of gauge conformal invariance.
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