Hyperbolic Geometry

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


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.


Lorentz Transformation Vector Subspace Hyperbolic Geometry Geodesic Line Hyperbolic Line 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

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

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