TY - JOUR

T1 - Graph manifolds as ends of negatively curved riemannian manifolds

AU - FUJIWARA, KOJI

AU - SHIOYA, TAKASHI

N1 - Publisher Copyright:
Copyright © 2019, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2019/3/17

Y1 - 2019/3/17

N2 - 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.

AB - 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.

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