Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2 Dimensional Riemannian Manifolds

Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2 Dimensional Riemannian Manifolds

Author
Takashi Shioya
Publisher
Amer Mathematical Society
Language
English
Year
1994
Page
73
ISBN
082182578X,9780821825785
File Type
pdf
File Size
6.1 MiB

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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