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Article Dans Une Revue Journal of Geometry and Physics Année : 2019

Topological and geometric obstructions on Einstein–Hilbert–Palatini theories

Résumé

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 condition for k = 1 and s = 2, including Hitchin's generalized complex geometry , Pantilie's generalized quaternionic geometries and all other generalized Cayley-Dickson geometries. We also prove that if A is concrete in some sense, then a torsionless version of A-EHP is non-null only if M is Kähler of dimension n = 2, 4. We present our results as obstructions to M being an Einstein manifold relative to geometries other than semi-Riemannian.
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Dates et versions

hal-02907885 , version 1 (27-07-2020)

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Yuri Ximenes Martins, Rodney Josué Biezuner. Topological and geometric obstructions on Einstein–Hilbert–Palatini theories. Journal of Geometry and Physics, 2019, 142, pp.229-239. ⟨10.1016/j.geomphys.2019.04.012⟩. ⟨hal-02907885⟩

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