Let M be a graph manifold such that each piece of its JSJ decomposition has the H2 ☓R geometry. Assume that the pieces are glued by isometries. Then there exists a complete Riemannian metric on R ☓ M which is an “eventually warped cusp metric” with the sectional curvature K satisfying 1 < K < 0. A theorem by Ontaneda then implies that M appears as an end of a 4–dimensional, complete, noncompact Riemannian manifold of finite volume with sectional curvature K satisfying 1 < K < 0.
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