TY - JOUR

T1 - Graph manifolds as ends of negatively curved riemannian manifolds

AU - Fujiwara, Koji

AU - Shioya, Takashi

N1 - Funding Information:
The authors are partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science, 15H05739, 26400060, 19K03459, 20H00114.

PY - 2020

Y1 - 2020

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, noncompact 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, noncompact Riemannian manifold of finite volume with sectional curvature K satisfying 1 < K < 0.

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U2 - 10.2140/gt.2020.24.2035

DO - 10.2140/gt.2020.24.2035

M3 - Article

AN - SCOPUS:85096669923

VL - 24

SP - 2035

EP - 2074

JO - Geometry and Topology

JF - Geometry and Topology

SN - 1465-3060

IS - 4

ER -