Supergravity Tensor Calculus in 5D from 6D

Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus still retains the dilatation gauge symmetry so that it becomes a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system.Comment: 38 pages, no figures, LaTeX, version to appear in PTP 104(2000),835-86

Review of some classical gravitational superenergy tensors using computational techniques

We use computational algorithms recently developed by us to study completely four index divergence free quadratic in Riemann tensor polynomials in GR. Some results are new and some other reproduce and/or correct known ones. The algorithms are part of a Mathematica package called Tools of Tensor Calculus (TTC)[web address: http://baldufa.upc.es/ttc

Exceptional geometry and tensor fields

We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E_n(n). We then consider "tensor gauge fields" coupled to the exceptional generalised gravity. Many of the properties of forms on manifolds are carried over to these fields.Comment: 22 pp., plain tex. v3: improved reference