Parametric Manifolds II: Intrinsic Approach

Details Parametric Manifolds II: Intrinsic Approach Parametric Manifolds II: Intrinsic Approach

1994-07-12

arxiv.org/abs/gr-qc/9407012v1

J.Math.Phys. 36 (1995) 1394-1403

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Plain TeX, 13 pages, no figures

Scientific paper

10.1063/1.531128

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) 1-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 1-parameter family of orthogonal hypersurfaces.

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