Cquasigeodesic

A cquasigeodesic is a curve in a Riemannian manifold that approximates a geodesic in a specific sense. Unlike a true geodesic, which is a path of locally shortest length between two points, a cquasigeodesic may deviate from the shortest path, but this deviation is controlled and bounded.

The concept arises in the study of geometric structures where exact geodesics might be difficult to define or may not possess desirable properties. Cquasigeodesics offer a more flexible alternative for analyzing paths and distances within such spaces. They are often defined by a differential inequality that limits how far a cquasigeodesic can stray from a true geodesic.

In essence, a cquasigeodesic is a curve whose path is "almost" a geodesic. This "almost" is quantified, ensuring that the curve does not wander arbitrarily. The precise definition and properties of cquasigeodesics depend on the specific context and the type of geometric structure being considered. They find applications in areas such as hyperbolic geometry, the study of metric spaces, and geometric group theory.