Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2-dimensional Riemannian Manifolds (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Shioya, Takashi

 
9780821825785: Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2-dimensional Riemannian Manifolds (Memoirs of the AMS) (Memoirs of the American Mathematical Society)

Synopsis

This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many
illustrations that enhance understanding of the main ideas.

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