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Parametric Manifolds II: Intrinsic Approach | | Stuart Boersma
; Tevian Dray
; | | Date: |
12 Jul 1994 | | Journal: | J.Math.Phys. 36 (1995) 1394-1403 | | Subject: | General Relativity and Quantum Cosmology; Differential Geometry | gr-qc dg-ga math.DG | | Abstract: | 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. | | Source: | arXiv, gr-qc/9407012 | | Services: | Forum | Review | PDF | Favorites | |
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