Abstract
Various kinematical relations, holding between hypersurface projections of spacetime tensor fields in an arbitrary Riemannian spacetime, are studied in terms of differential geometry in hyperspace. A criterion is given that a collection of hypertensor fields is generated by the projections of a single spacetime tensor field intersected by the embeddings. From here, it is shown that the super-Hamiltonian of an arbitrary tensor field splits into two parts, Hφ↑ and Hφ−, Hφ↑ being local in the field momenta and Hφ− containing their first derivatives. The form of Hφ− for an arbitrary tensor field is determined from the field behavior under hypersurface tilts. The kinematical equations for the intrinsic metric and the extrinsic curvature are written in a quasicanocical form, and their connection with the closing relations for the gravitational super-Hamiltonian is exhibited. The conservation laws of charge, energy and momentum, and the contracted Bianchi identities, are written as hypertensor equations.
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