Length product of homologically independent loops for tori

Abstract

We prove that any Riemannian torus of dimension $m$ with unit volume admits $m$ homologically independent closed geodesics whose length product is bounded from above by $m^m$.

References in corpus (1)

• On Isosystolic Inequalities for T^n, RP^n, and M^3

Cited by in corpus (1)

• Minimal length product over homology bases of manifolds