Abstract
We 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, admits the standard metric g 0 as a critical point, although it does 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 increase.
| Translated title of the contribution | On the systole of the sphere in the proximity of the standard metric |
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| Original language | French |
| Pages (from-to) | 61-71 |
| Number of pages | 11 |
| Journal | Geometriae Dedicata |
| Volume | 121 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Aug 2006 |