The systolic constant of orientable Bieberbach 3-manifolds

Autor:	Elmir, Chady, Lafontaine, Jacques
Rok vydání:	2009
Předmět:	Mathematics - Differential Geometry Mathematics - Geometric Topology 53C23-53C22-53C20
Zdroj:	Annales de la facult\'e des sciences de Toulouse S\'er. 6, 22 no. 3 (2013), p. 623-648
Druh dokumentu:	Working Paper
Popis:	A compact manifold is called Bieberbach if it carries a flat Riemannian metric. Bieberbach manifolds are aspherical, therefore the supremum of their systolic ratio, over the set of Riemannian metrics, is finite by a fundamental result of M. Gromov. We study the optimal systolic ratio of compact of $3$-dimensional orientable Bieberbach manifolds which are not tori, and prove that it cannot be realized by a flat metric. We also highlight a metric that we construct on one type of such manifolds ($C_2$) which has interesting geometric properties : it is extremal in its conformal class and the systole is realized by "very many" geodesics. Comment: 18 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0912.3894 Zobrazit plný text záznamu View this record from Arxiv