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- W2888822998 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 condition for k=1 and s=2, including Hitchin’s and Gualtieri’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." @default.
- W2888822998 created "2018-09-07" @default.
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- W2888822998 date "2019-08-01" @default.
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- W2888822998 title "Topological and geometric obstructions on Einstein–Hilbert–Palatini theories" @default.
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- W2888822998 doi "https://doi.org/10.1016/j.geomphys.2019.04.012" @default.
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