In this paper we prove that solutions of the f-plane approximation for
equatorial geophysical deep water waves, which have the property that the
pressure is constant along the streamlines and do not possess stagnation
points,are Gerstner-type waves. Furthermore, for waves traveling over a flat
bed, we prove that there are only laminar flow solutions with these properties.Comment: To appear in Journal of Nonlinear Mathematical Physics; 15 page