Einstein warped products in 4D are classified algebraically via curvature matrix blocks into Petrov types (3+1 generically type I, 2+2 type D, 1+3 type O), with closed Riemannian half-conformally flat cases required to be flat.
Compact four-dimensional Einstein manifolds
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For each odd integer p > 1, infinitely many pairwise non-diffeomorphic irreducible smooth structures are constructed on a definite 4-manifold with infinite fundamental group whose abelianization is Z/2pZ × Z/2Z.
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Warped Product Einstein Manifolds in Four Dimensions
Einstein warped products in 4D are classified algebraically via curvature matrix blocks into Petrov types (3+1 generically type I, 2+2 type D, 1+3 type O), with closed Riemannian half-conformally flat cases required to be flat.
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Smooth structures on definite four-manifolds with infinite fundamental group
For each odd integer p > 1, infinitely many pairwise non-diffeomorphic irreducible smooth structures are constructed on a definite 4-manifold with infinite fundamental group whose abelianization is Z/2pZ × Z/2Z.