Intrinsic Directions, Orthogonality and Distinguished Geodesics in the Symmetrized Bidisc

Jim Agler, Zinaida Lykova, N. J. Young

The symmetrized bidisc \[ G \stackrel{\rm{def}}{=}\{(z+w,zw):|z|<1,\ |w|<1\}, \] under the Carathéodory metric, is a complex Finsler space of cohomogeneity $1$ in which the geodesi…