  We investigate the ground-state property of an e_g-orbital Hubbard model at
quarter filling on a zigzag chain by exploiting the density matrix
renormalization group method. When two orbitals are degenerate, the zigzag
chain is decoupled to a doble-chain spin system to suppress the spin
frustration due to the spatial anisotropy of the occupied orbital. On the other
hand, when the level splitting is increased and the orbital anisotropy
disappears, a characteristic change in the spin incommnsurability is observed
due to the revival of the spin frustration.
