  The CR $\delta$-invariant for CR-submanifolds was introduced in a recent
article [B. Y. Chen, An optimal inequality for CR-warped products in complex
space forms involving CR $\delta$-invariant, Internat. J. Math. 23} (2012), no.
3, 1250045 (17 pages)]. In this paper, we prove two new optimal inequalities
for anti-holomorphic submanifolds in complex space forms involving the CR
$\delta$-invariant. Moreover, we obtain some classification results for certain
anti-holomorphic submanifolds in complex space forms which satisfy the equality
case of either inequality.
