Sur la systole de la sph\`{e}re au voisinage de la m\'{e}trique standard
Differential Geometry
2007-05-23 v1 Dynamical Systems
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, have the standard metric 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 , there exists a variation by metrics corresponding to this direction along which the systolic area can only increase
Cite
@article{arxiv.math/0601285,
title = {Sur la systole de la sph\`{e}re au voisinage de la m\'{e}trique standard},
author = {Florent Balacheff},
journal= {arXiv preprint arXiv:math/0601285},
year = {2007}
}
Comments
12 pages