The Castelnuovo-Mumford regularity r of the variety V contained in a projective space P, n, k is an upper bound for the degrees of the hypersurfaces necessary to cut out V. In this work we give a bound for r when V is an arithmetically Cohen-Macaulay and sub-canonical curve which is invariant by a vector field on projective space P, n, k with coefficients in an invertible sheaf, under some conditions on the field k. Furthermore, we give a bound for r (i.e.for the degree of the V) when V is a hypersurface solution of the Pfaff equation of the rank 1, under some conditions on the field k. In both limits we consider the positions of the singularities of the V. These limits are the generalizations of the bounds given by E. Esteves in [17].