The method comprises providing a piece of flat metal sheet (110); shaping said piece of flat metal sheet (110) by means of conical rolling or stamping to achieve the form of a partially formed piece (120) composed of a plate (1), a provisional hollow portion (2a) extending from said plate (1) with an axisymmetrical form about an axis (E) perpendicular to the plate (1), and an end wall (3) closing an end of said provisional hollow portion (2a) opposite the plate (1); and lengthening a section of the provisional hollow portion (2a) by means of conical or cylindrical rolling. The absorber (130) is as a single piece with a plate (1) and an elongate hollow portion (2b), which extends from the plate (1) with an axisymmetrical form. A section of the elongate hollow portion (2b) has a thickness (Gf) that is thinner than the thickness (Gi) of the plate (1).
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