Bounded 3-manifolds admit negatively curved metrics with concave boundary. (English) Zbl 0821.53035

Hass, Joel

J. Differ. Geom. 40, No. 3, 449-459 (1994).

A metric can be constructed on any 3-manifold with non-empty boundary such that with respect to the metric the manifold has negative sectional curvature and the boundary is concave. In particular, the 3-ball admits such a metric.

Reviewer: J.Hass

MSC:

53C20	Global Riemannian geometry, including pinching
57R55	Differentiable structures in differential topology

Keywords:

concave boundary; manifold with boundary; 3-manifold; negative sectional curvature