The geometry of filiform nilpotent Lie groups
type: Item
instance of: scholarly article
title: The geometry of filiform nilpotent Lie groups
zbMATH Open document ID: 1206.53058
DOI: 10.1216/RMJ-2010-40-5-1587
author: Megan M. Kerr
author: Tracy L. Payne
published in: Rocky Mountain Journal of Mathematics
publication date: 2010-12-21T00:00:00Z
review text: The authors study the geometry of a filiform nilpotent Lie group endowed with a left-invariant metric. This is a contribution to the geometry of higher-step nilpotent Lie groups. A filiform is an \(n\)-dimensional nilpotent Lie group for which the lower central series of its corresponding Lie algebra is as long as possible, having \(n-2\) nontrivial subalgebras. That is, an \(n\)-dimensional filiform Lie algebra is \((n-1)\)-step. They describe the connection and curvatures, and they investigate necessary and sufficient conditions for subgroups to be totally geodesic submanifolds. They also classify one-parameter subgroups which are geodesics.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 22F30
zbMATH DE Number: 5828483
zbMATH Keywords: filiform
zbMATH Keywords: nilmanifold
zbMATH Keywords: totally geodesic submanifold
Wikidata QID: Q115240037
reviewed by: Andreas Arvanitoyeorgos
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5828483