, Volume 23, Issue 1, pp 1-14
Date: 06 Jun 2012

Projective Cross-ratio on Hypercomplex Numbers

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Abstract

The paper presents a new cross-ratio of hypercomplex numbers based on projective geometry. We discuss the essential properties of the projective cross-ratio, notably its invariance under Möbius transformations. Applications to the geometry of conic sections and Möbiusinvariant metrics on the upper half-plane are also given.