An applicator used to apply a cosmetic composition to the eyelashes or the eyebrows includes a stem having a distal stem portion extending along a longitudinal axis and further includes a brush extending from the distal stem portion. The brush includes a core supporting bristles. The core extends along a longitudinal axis that is entirely contained within a plane. The core further has a first curve that is concave towards a first side of the core and a second curve, different from the first curve, that is concave towards a second side of the core opposite from the first side of the core. The longitudinal axis of the core crosses the longitudinal axis of the distal stem portion at least once. The core of the brush extends along the longitudinal axis of the core towards a free end of the core without turning back towards the distal stem portion.