Intrinsic study of generalized horizontal recurrent Finsler connection

The present paper provides an intrinsic generalization of a horizontally recurrent Finsler connection, which we call the generalized horizontally recurrent Finsler connection ($\operatorname{GHRF}\Gamma$). We establish a proof of the uniqueness and existence theorem of $\operatorname{GHRF}\Gamma$, investigate relations between the curvature and torsion tensors of Cartan and $\operatorname{GHRF}\Gamma$, and study some geometric consequences and special cases of $\operatorname{GHRF}\Gamma$. We give an example in some details with a special case.