surface with gathering mechanisms of this area these gathering mechanisms making it possible to remodel the curve of this cap in order to adjust it closely to the shape of the skull of the person using it for example the cap is equipped with gathering mechanisms in one or more of the following areas the gathering mechanisms are preferably arranged and distributed in the areas of the surface inside the surface intended to cover the occipital regions o and temporal regions t of the skull the gathering mechanisms can be made up of a plurality of complementary devices for adjustment making it possible to modify the distance between different points of the structure of the cap in a manner so as to remodel the curve of the cap according to the example shown in fig2 to 6 these complementary mechanisms for adjustment comprise a plurality of flexible brackets 9 affixed by means of one of their ends to the structure of the cap and the other end of which is equipped with a point of attachment 10 in an advantageous manner these adjusting brackets can be comprised of a narrow band of non slip stretchable fabric such as the one described in the document wo 99 44452 on the other.