The local geometry of Carnot manifolds at singular points
type: Item
instance of: scholarly article
title: The local geometry of Carnot manifolds at singular points
zbMATH Open document ID: 1235.53037
DOI: 10.3103/S1066369X11080135
published in: Russian Mathematics
publication date: 2011-11-21T00:00:00Z
review text: The author considers a Carnot manifold whose defining vector fields are minimally smooth. It is stated that the local geometry of such manifolds is similar to the case when the defining vector fields are \(C^\infty\), i.e., the Rashevskii-Chow theorem holds (points can be joined by horizontal curves), and the tangent cone is constructed. The results include the case where the Carnot manifold may contain singular points. This version of the paper does not contain proofs of the results.
reviewed by: Nathaniel Eldredge
Mathematics Subject Classification ID: 53C17
zbMATH DE Number: 5975561
zbMATH Keywords: Carnot manifold
zbMATH Keywords: minimal smoothness
zbMATH Keywords: Rashevskii-Chow theorem
zbMATH Keywords: tangent cone
zbMATH Keywords: Carnot group
author: Svetlana V. Selivanova
MaRDI profile type: Publication
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full work available at URL: s1066369x11080135
OpenAlex ID: W1982881149
description: scientific article; zbMATH DE number 5975561