On geodesic bifurcations of product spaces

The bifurcation is described as a situation where there exist at least two different geodesics going through the given point in the given direction. In the previous works, the examples of local and closed bifurcations are constructed. This paper is devoted to the further study of these bifurcations. We construct an example of n -dimensional (pseudo-) Riemannian and Kählerian spaces which are product ones that admit a local bifurcation of geodesics and also a closed geodesic.