Einstein–Kähler Metric with Explicit Formula on Super–Cartan Domain of the Fourth Type

Abstract

Let YIV be the Super–Cartan domain of the fourth type. We reduce the Monge–Ampere equation for the metric to an ordinary differential equation in the auxiliary function X = X(Z,W). This differential equation can be solved to give an implicit function in X. We give the generating function of the Einstein–Kahler metric on YIV . We obtain the explicit form of the complete Einstein–Kahler metric on YIV for a special case.