A new intrinsic metric called t-metric is introduced. Several sharp
inequalities between this metric and the most common hyperbolic type metrics
are proven for various domains GβRn. The behaviour of the
new metric is also studied under a few examples of conformal and quasiconformal
mappings, and the differences between the balls drawn with all the metrics
considered are compared by both graphical and analytical means.Comment: 20 pages, 8 figure