2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123052We study the systolic area (defined as the ratio of the area over the square of the systole) of the 2-sphere endowed with a smooth riemannian metric as a function of this metric. This function, bounded from below by a positive constant over the space of metrics, have the standard metric $g\_0$ for critic point, although this one do not achieve the conjectured global minimum : we show that for each tangent direction to the space of metrics at $g\_0$, there exists a variation by metrics corresponding to this direction along which the systolic area can only increase12 pagesDifferential GeometryDynamical Systems53B20, 37C27text