Advertisement

Hyperbolic Geometry

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

Abstract

We now begin the study of hyperbolic geometry. The first step is to define a new inner product on ℝ n , called the Lorentzian inner product. This leads to a new concept of length. In particular, imaginary lengths are possible. In Section 3.2, hyperbolic n-space is defined to be the positive half of the sphere of unit imaginary radius in ℝ n+1. The elements of hyperbolic arc length and volume are determined in Sections 3.3 and 3.4. The chapter ends with a section on hyperbolic trigonometry.

Keywords

Lorentz Transformation Vector Subspace Hyperbolic Geometry Geodesic Line Hyperbolic Line 
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