
We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.
Mathematics - Differential Geometry, Goldberg conjecture, Sasakian-Einstein, contact metric manifold, Sasakian manifold, \(K\)-contact Einstein manifold, Special Riemannian manifolds (Einstein, Sasakian, etc.), Differential Geometry (math.DG), Mathematics - Symplectic Geometry, FOS: Mathematics, Contact manifolds (general theory), Symplectic Geometry (math.SG)
Mathematics - Differential Geometry, Goldberg conjecture, Sasakian-Einstein, contact metric manifold, Sasakian manifold, \(K\)-contact Einstein manifold, Special Riemannian manifolds (Einstein, Sasakian, etc.), Differential Geometry (math.DG), Mathematics - Symplectic Geometry, FOS: Mathematics, Contact manifolds (general theory), Symplectic Geometry (math.SG)
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