Graph manifolds as ends of negatively curved Riemannian manifolds

Fujiwara, Koji¹ ; Shioya, Takashi²

¹ Department of Mathematics, Kyoto University, Kyoto, Japan
² Mathematics Institute, Tohoku University, Sendai, Japan

Geometry & topology, Tome 24 (2020) no. 4, pp. 2035-2074.

Résumé

Let $M$ be a graph manifold such that each piece of its JSJ decomposition has the ${ℍ}^2\times ℝ$ geometry. Assume that the pieces are glued by isometries. Then there exists a complete Riemannian metric on $ℝ\times M$ which is an “eventually warped cusp metric” with the sectional curvature $K$ satisfying $-1\le K<0$.

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 $-1\le K<0$.

Détail

DOI : 10.2140/gt.2020.24.2035

Classification : 53C20, 57M50, 57N10
Keywords: ends of manifolds, negative curvature, graph manifold, cusp

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