2021/06/19 by Michael R. Pilla, Pilla, Michael R.
Decision Sciences · Mathematics · #32A08 #Advanced Statistical Methods and Models #Complex Variables (math.CV) #FOS: Mathematics #Multi-Criteria Decision Making #Optimal Experimental Design Methods
paper · pdf · doi:10.48550/arxiv.2106.10570
openalex publication_date 2021/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In one complex variable, the cross ratio is a well-known quantity associated with four given points in the complex plane that remains invariant under linear fractional maps. In particular, if one knows where three points in the complex plane are mapped under a linear fractional map, one can use this invariance to explicitly determine the map and to show that linear fractional maps are 3-transitive. In this paper, we define a generalized cross ratio and determine some of its basic properties. In particular, we determine which hypotheses must be made to guarantee that our generalized cross ratio is well defined. We thus obtain a class of maps that obey similar transitivity properties as in one complex dimension, under some more restrictive conditions.