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, non-compact Riemannian manifold of finite volume with sectional curvature K satisfying -1 ≤ K < 0.
|Publication status||Published - 2019 Mar 17|
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