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.Comment: Plain TeX, 13 pages, no figure
