A study of the most general Lagrangian functions for which field equations of Variant Field Theory are such that geometric object fields comprising the dependent variable set are invariant under a finite continuous group of coordinate transformations. The arguments are based on the concept of a geometry class. This enables the results to be cast in as general a context as possible yet allowing the derivation of specific systems of partial differential equations whose solution manifolds span the class of admissible Lagrangian functions. 40 pp
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