Linear connections compatible with the $F(3,1)$-structure on the

Abstract

In this paper the $F$-structure, satisfying $F^{3}+F=0$ on the Lagrangian space, is examined. The construction of this structure is given as the prolongation of $f_{v}$-structure defined on $T_{V}(E)$ using the almost product or almost complex structure on $T(E)$. Moreover, the metric tensor $G$, with respect to which $F$ is an isometry, is constructed as well as the connection compatible with such structures.