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.