On $bar {G}$-$J$ Anti-invariant Submanifolds of Almost Complex Contact Metric Manifolds

In this article we studied anti-invariant submanifolds of almost complex contact metric manifolds. We found a relation between Nijenhuis tensor fields of anti-invariant submanifolds and almost complex contact manifolds. We investigated relations between curvature tensors of these manifolds. Moreover, we studied anti-invariant submanifolds of almost complex contact metric manifolds.Some necessary conditions on which a submanifolds of an almost complex contact metric manifolds is $bar {G}$-$J$ anti-invariant were given. Also we found some characterizations for totally geodesic or umbilical $bar {G}$-$J$ anti-invariant submanifolds of almost complex contact metric manifolds.