Almost Golden Structures, Nonlinear Connections and Sprays

We introduce and investigate a special class of almost golden structures on the tangent bundle TM of a smooth manifoldM. It is shown that there is a one-to-one correspondence between the nonlinear connection and the special almost golden structure on the tangent bundle. Moreover, there is a one-to-one correspondence between sprays and homogeneous special almost golden strictures. Finally, the question of integrability of almost golden structures is discussed and certain characterizations of integrability are found out.