The filling radius of homogeneous manifolds. (English) Zbl 0742.53012

Katz, Mikhail

Sémin. Théor. Spectrale Géom., Chambéry-Grenoble 9, Année 1990-1991, 103-109 (1991).

The notion of the filling radius \(\text{Fill Rad}(V^ n)\) of an \(n\)-dimensional Riemannian manifold \((V^ n,g)\) was introduced by M. Gromov for the proof of the isosystolic inequality [J. Differ. Geom. 18, 1-147 (1983; Zbl 0515.53037)]. In this paper the author studies a question about the filling radius of some homogeneous manifolds. In particular, he obtains upper bounds for the integer filling radius of complex projective spaces and lens spaces and shows that \(\text{Fill Rad}({\mathbb{C}}P^ n,{\mathbb{Q}})=(1/2)\arccos (-1/32)\).

Reviewer: E.D.Rodionov (Barnaul)

MSC:

53C20	Global Riemannian geometry, including pinching
53C30	Differential geometry of homogeneous manifolds
53C23	Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces

Keywords:

filling radius; homogeneous manifolds; complex projective spaces; lens spaces

Citations:

Zbl 0515.53037