Geometric Surfaces

  • John G. Ratcliffe
Part of the Graduate Texts in Mathematics book series (GTM, volume 149)

Abstract

In this chapter, we study the geometry of geometric surfaces. The chapter begins with a review of the topology of compact surfaces. In Section 9.2, a geometric method for constructing spherical, Euclidean, and hyperbolic surfaces is given. The fundamental relationship between the Euler characteristic of a closed geometric surface and its area is derived in Section 9.3. In Section 9.4, the set of similarity equivalence classes of Euclidean or hyperbolic structures on a closed surface is shown to have a natural topology. The geometry of closed geometric surfaces is studied in Sections 9.5 and 9.6. The chapter ends with a study of the geometry of complete hyperbolic surfaces of finite area.

Keywords

Modulus Space Closed Geodesic Geometric Surface Klein Bottle Hyperbolic Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • John G. Ratcliffe
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

Personalised recommendations