A \((J^ 4=1)\)-structure on an \(n\)-dimensional manifold \(M\) is a tensor field of type \((1,1)\) on \(M\) such that \(J^ 4=1\). Its characteristic polynomial is \((x-1)^{r_ 1}(x+1)^{r_ 2}(x^ 2+1)^ s\), where \(r_ 1+r_ 2+s=n\). In particular, one obtains the almost complex structure, the almost product structure and the almost hyperbolic complex structure (i.e. \(J^ 2=1\), \(J\neq \pm 1\) and \(r_ 1=r_ 2)\). Moreover, a \((J^ 4=1)\)-structure is metric if there is a pseudo-Riemannian structure \(g\) on \(M\) such that either (1) \(J\) is symmetric with respect to \(g\) or (2) \(J\) is skew- symmetric with respect to \(g\). In particular, one gets the almost Hermitian structure, the almost Riemannian product structure,the almost hyperbolic Hermitian structure (i.e. \(J^ 2-1\) and \(g\) satisfy (2) [\textit{P. Libermann}, Ann. Mat. Pura Appl., IV. Ser. 36, 27--120 (1954; Zbl 0056.15401)], \(e\)-metric \((J^ 4=1)\)-structure (i.e. \(J^ 4=1\) and \(g\) satisfies (2)). An \(e\)-metric \((J^ 4=1)\)-manifold is an \(e\)-(J\({}^ 4=1)\)-Kähler one if \({\bar \nabla}J=0\), where \({\bar \nabla}\) is the Levi-Cività connection of \(g\). The particular case when \(J^ 2=1\) was introduced by \textit{P. K. Rashevskii} [Tr. Semin. Vektorn. Tenzorn. Anal. 6, 225--248 (1948)]. In the present paper, the \(e-(J^ 4=1)\)-Kähler manifolds of constant \(J\)-sectional curvature are studied by extending the case exposed by \textit{M. S. Prvanović} [Math. Balk. 1, 195--213 (1971; Zbl 0221.53062)] and a theorem of Schur type is given. Also, it is shown that any two complex connected and simply connected \(e-(J^ 4=1)\)-Kähler manifolds of constant and equal \(J\)-sectional curvature are \(J\)-isometric. Models of para-Kähler manifolds are constructed here. As an \(e-(J^ 4=1)\)-Kähler manifold is locally the product of a hyperbolic Kähler manifold and a Kähler manifold, it follows that some models of \(e-(J^ 4=1)\)-Kähler manifolds can be obtained.