Abstract
We consider surfaces of negative extrinsic curvature in a
Riemannian space with nonpositive curvature. We prove that the following
inequality holds on a surface which is complete in the sense of the intrinsic
metric:
here F is the surface being considered, 
(Ke is the extrinsic curvature
of F) and Λ and λ are the maximum and minimum of the Riemannian curvature
of the space R at a given point.
This theorem generalizes a theorem of Efimov concerning q-metrics. We
give an example of a surface for which q=4.5.
Bibliography: 8 items.