Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.
Lorentzian Cayley Form
3 Pith papers cite this work. Polarity classification is still indexing.
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Explicit construction of the Plebanski matter source T^i via Kulkarni-Nomizu lifting of the trace-free energy-momentum tensor that reproduces Krasnov's definition and yields the Reissner-Nordström-de Sitter solution.
Plebanski's chiral 2-form formulation of GR reveals additional structure in Einstein's equations and supplies new analytical and numerical tools.
citing papers explorer
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On the rigidity of special and exceptional geometries with torsion a closed $3$-form
Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.
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On the Plebanski Formulation with Energy Momentum
Explicit construction of the Plebanski matter source T^i via Kulkarni-Nomizu lifting of the trace-free energy-momentum tensor that reproduces Krasnov's definition and yields the Reissner-Nordström-de Sitter solution.
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General Relativity via differential forms -- explorations in Plebanski's Formalism for GR
Plebanski's chiral 2-form formulation of GR reveals additional structure in Einstein's equations and supplies new analytical and numerical tools.