Notes on Relative Contact Equivalence of Complex Analytic Map-Germs

In these notes, our goal is to give some results on criterion for complex analytic map-germs by their tangent spaces with respect to Θ^ĸ-equivalence where Θ is the module of complex analytic vector fields on (¢^n,0).In addition, we give some results about Θ^ĸ-trivial analytic family, the direct product and direct sum of map-germs.