Parametric manifolds. II. Intrinsic approach Public Deposited

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  • A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) one‐form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, all based on a nonstandard action of vector fields on functions. There is a new geometric object, called the deficiency, which behaves much like torsion, and which measures whether a parametric manifold can be viewed as a one‐parameter family of orthogonal hypersurfaces.
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  • Boersma, S., & Dray, T. (1995, March). Parametric manifolds. II. Intrinsic approach. Journal of Mathematical Physics, 36(3), 1394-1403. doi:10.1063/1.531129
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