Actually my main concern is contact geometry but maybe you can find some in Mirjana Djoric book and papers

For a complex submanfold M of a non-Kaehlerian manifold N, the Gauss and Weingarten equations are the same as for a general submanifold of a Riemannian manifold, unless you impose some condition of the ambient space, for example, a nearly-Kaehlerian condition or other condition so that we have some information on the covariant derivative of the almost complex structure on the ambient space.