Conformal isosystolic inequality of Bieberbach 3-manifolds
Mir, Chady El
arXiv, 1007.0877 / Harvested from arXiv
Text on arXiv
The systole of a compact non simply connected Riemannian manifold is the smallest length of a non-contractible closed curve ; the systolic ratio is the quotient $(\mathrm{systole})^n/\mathrm{volume}$. Its supremum, over the set of all Riemannian metrics, is known to be finite for a large class of manifolds, including aspherical manifolds. We study a singular metric $g_0$ which has a better systolic ratio than all flat metrics on $3$-dimensional non-orientable Bieberbach manifolds (introduced in [El-La08]), and prove that it is extremal in its conformal class.
Publié le : 2010-07-06
Classification:  Mathematics - Differential Geometry 
@article{1007.0877,
     author = {Mir, Chady El},
     title = {Conformal isosystolic inequality of Bieberbach 3-manifolds},
     journal = {arXiv},
     volume = {2010},
     number = {0},
     year = {2010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1007.0877}
}

Mir, Chady El. Conformal isosystolic inequality of Bieberbach 3-manifolds. arXiv, Tome 2010 (2010) no. 0, . http://gdmltest.u-ga.fr/item/1007.0877/