This article is cited in 1 paper

Systoles on Heisenberg groups with Carnot–Carathéodory metrics

V. V. Dontsov

M. V. Lomonosov Moscow State University

Abstract: The systolic properties of the nilmanifolds $\mathscr N^{2n+1}$ associated with the higher Heisenberg groups $H_{2n+1}$ are studied. Effective estimates of the systolic constants $\sigma(\mathscr N^{2n+1})$ in the Carnot–Carathéodory geometry, as functions of the parameters defining a uniform lattice on $H_{2n+1}$, are obtained.

UDC: 514.174.6

MSC: Primary 53C30, 53D10, 53D35; Secondary 53C20

Received: 01.06.2000

DOI: 10.4213/sm549

 English version: Sbornik: Mathematics, 2001, 192:3, 347–374

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