Authors explicitly construct the Einstein connection for G = g + F via a weak almost contact structure (f, ξ, η) satisfying g(X, fY) = F(X, Y) and a natural condition.
A new nonsymmetric gravitational theory, Physics Letters B, 355, (1995), 447-452
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Einstein connection of nonsymmetric pseudo-Riemannian manifold, II
Authors explicitly construct the Einstein connection for G = g + F via a weak almost contact structure (f, ξ, η) satisfying g(X, fY) = F(X, Y) and a natural condition.