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We introduce the notion of a manifold admitting a simple compact Cartan 3-form ω3. We study algebraic types of such manifolds, in particular those having skew-symmetric torsion, or those associated with a closed or coclosed 3-form ω3. We prove the existence of an algebra of multi-symplectic forms ϕl on these manifolds. Cohomology groups associated with complexes of differential forms on Mn in the...
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