## Manifolds of non-positive curvature.(English)Zbl 0712.53019

The article gives an introduction to the geometry of manifolds of negative curvature (presentation of symmetric and homogeneous examples, basic properties of geodesics and Jacobi fields) and presents an overview over some of the recent results in this area. A sketch of proof of the following rigidity result of Gromov is included: A metric of nonpositive curvature on $$R^ n$$ which is flat outside a compact set is flat.
Reviewer: U.Hamenstädt

### MSC:

 53C20 Global Riemannian geometry, including pinching 53-02 Research exposition (monographs, survey articles) pertaining to differential geometry

### Keywords:

flats; negative curvature; geodesics; Jacobi fields; rigidity result