%0 Journal Article %T A Model for the HyperKahler Metrics Building Program %A A. El Boukili %A A. Zemate %A M.B. sedra %J - %D 2012 %R 10.14419/ijbas.v1i4.362 %X Its by now well known that the harmonic superspace provides astrong framework for constructing general hyperKahler metrics. Origi-nal results in this issue are given by the Taub-Nut and Egushi-Hansonmetrics exhibiting both U(1) Pauli-Gursey isomertie as shown by Gib-bon et all in [1]. Its also shown that there exist series of potentialdepending explicitly on the harmonics variables u on the sphere S2.Based on these knowledge and on previous contributions to the pro-gram of metrics building [2, 3], we contribute by presenting a specialhyperKahler potential H+4 leading to an -parametrized Liouville equa-tion on the harmonic superspace. %U https://www.sciencepubco.com/index.php/ijbas/article/view/362