Systoles of nilmanifolds with the Carnot-Caratheodory metrics
type: Item
instance of: scholarly article
title: Systoles of nilmanifolds with the Carnot-Caratheodory metrics
zbMATH Open document ID: 1036.53027
DOI: 10.1023/A:1021194109447
author: V. V. Dontsov
published in: Journal of Mathematical Sciences (New York)
publication date: 2003-09-01T00:00:00Z
full work available at URL: https://eudml.org/doc/222890
review text: Let \((X, \rho)\) be a metric space of Hausdorff dimension \(m\) with an inner metric \(\rho\). The systolic constant of \(X\) is the infimum over all inner metrics on \(X\) of the quotient of the \(m\)-dimensional Hausdorff volume of \(X\) and the \(m\)-th power of the smallest length of homotopy nontrivial closed loops on \(X\). Such constant is homotopy invariant for Riemannian manifolds and it is very difficult to compute. In the present paper the author considers the class of nilmanifolds with the Carnot-Caratheodory metrics and obtains some estimates for the systolic constants of these metric spaces.
reviewed by: Anna Fino
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 1971318
zbMATH Keywords: systoles
zbMATH Keywords: nilmanifolds
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: systolic constant
zbMATH Keywords: Hausdorff volume
MaRDI profile type: Publication
OpenAlex ID: W153352576
description: scientific article; zbMATH DE number 1971318