Topological and geometric obstructions on Einstein–Hilbert–Palatini theories

@article{Martins2018TopologicalAG,
  title={Topological and geometric obstructions on Einstein–Hilbert–Palatini theories},
  author={Yuri Ximenes Martins and Rodney Josu{\'e} Biezuner},
  journal={Journal of Geometry and Physics},
  year={2018},
  volume={142},
  pages={229-239}
}
Abstract In this article we introduce A -valued Einstein–Hilbert–Palatini functional ( A -EHP) over a n -manifold M , where A is an arbitrary graded algebra, as a generalization of the functional arising in the study of the first order formulation of gravity. We show that if A is weak ( k , s ) -solvable, then A -EHP is non-null only if n k + s + 3 . We prove that essentially all algebras modeling classical geometries (except semi-Riemannian geometries with specific signatures) satisfy this… Expand

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