Glossary of Riemannian and Metric Geometry - Q

Q

Quasigeodesic has two meanings; here we give the most common. A map is called quasigeodesic if there are constants and such that

Note that a quasigeodesic is not necessarily a continuous curve.

Quasi-isometry. A map is called a quasi-isometry if there are constants and such that

and every point in Y has distance at most C from some point of f(X). Note that a quasi-isometry is not assumed to be continuous, for example any map between compact metric spaces is a quasi isometry. If there exists a quasi-isometry from X to Y, then X and Y are said to be quasi-isometric.