We get negative Gauss curvature K surfaces of quasi polar symmetry surface form generated from:

$$ Re  (x+ i y)^n =  a^n $$  (n  integer) with n humps above plane $ z =0$.

($ n =2,3,4 $  hyperbolic paraboloids, monkey saddles, four humped frill/ pleated shells respectively).

 "Quasi" due to $n>2$ introducing circumferential pleats or frills.

What polynomial or differential relation function  yields constant negative surfaces of  $K = -1/a^2 $?

How to set up its differential equation?