TL;DR
This paper introduces a novel projective cross-ratio for hypercomplex numbers, exploring its properties and applications in geometry and invariant metrics, expanding the mathematical tools for hypercomplex analysis.
Contribution
It proposes a new cross-ratio concept for hypercomplex numbers and examines its invariance and applications in geometric contexts.
Findings
The projective cross-ratio is invariant under Mobius transformations.
Applications to conic sections and Mobius-invariant metrics are demonstrated.
The paper extends classical cross-ratio concepts to hypercomplex settings.
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 Mobius transformations. Applications to the geometry of conic sections and Mobius-invariant metrics on the upper half-plane are also given.
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