Gravity in hyperspin manifolds

We seek the dynamics of a Bergmann manifold: a manifold of dimensionn=N ² supporting a bundle of spinor spaces of dimensionN, and a map from the tangent spaces to the Hermitian spinor forms. Even though the spin-vector is the fundamental variable of the theory, every invariant analytic function depending on and its firstm derivatives alone can be expressed in terms of the chronometric tensorg and its firstm derivatives. Bergmann manifolds of dimensionn > 4 do not have invariant second-order equations for. We find a family of invariant actions which lead tonth-order quasilinear equations of motion on Bergmann manifolds and reduce to the Einstein-Hilbert action forn=2. The resulting gauge particles have spin, 1/2,1, 3/2, and 2.