TITLE:
Hidden Symmetries of Complex Analysis
AUTHORS:
Cao-Huu Tuan, Dorin Ghisa, Allan Florin Muscutar
KEYWORDS:
Hidden Symmetry, Fundamental Domain, Antianalytic Involution
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.9 No.10,
October
15,
2019
ABSTRACT: We are dealing with domains of the complex plane which are not symmetric in common sense, but support fixed point free antianalytic involutions. They are fundamental domains of different classes of analytic functions and the respective involutions are obtained by composing their canonical projections onto the complex plane with the simplest antianalytic involution of the Riemann sphere. What we obtain are hidden symmetries of the complex plane. The list given here of these domains is far from exhaustive.