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Scientific article
Open access
French

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

Published inGeometriae dedicata, vol. 121, no. 1, p. 61-71
Collection
  • Open Access - Licence nationale Springer
Publication date2006
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 point
  • 2-sphere
  • Standard metric
  • Systole
  • Zoll metric
Citation (ISO format)
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
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Article (Published version)
accessLevelPublic
Identifiers
ISSN of the journal0046-5755
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