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Sur la systole de la sphère au voisinage de la métrique standard

Published in Geometriae Dedicata. 2006, vol. 121, no. 1, p. 61 - 71
Collection Open Access - Licence nationale Springer
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 g0 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 g0, there exists a variation by metrics corresponding to this direction along which the systolic area can only increase.
Keywords Critical point2-sphereStandard metricSystoleZoll metric
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BALACHEFF, Florent Nicolas. Sur la systole de la sphère au voisinage de la métrique standard. In: Geometriae Dedicata, 2006, vol. 121, n° 1, p. 61 - 71. doi: 10.1007/s10711-006-9087-7 https://archive-ouverte.unige.ch/unige:12125

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Deposited on : 2010-10-18

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