In 3D trans-Sasakian manifolds the Newman-Penrose equations encode the structure vector field via spin coefficients and prove that compatible structures on non-space-form E(κ,τ) metrics must be the canonical vertical ones.
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Newman--Penrose formalism in $3$-dimensional trans-Sasakian manifolds
In 3D trans-Sasakian manifolds the Newman-Penrose equations encode the structure vector field via spin coefficients and prove that compatible structures on non-space-form E(κ,τ) metrics must be the canonical vertical ones.