Generalized 2-symmetric submanifolds
type: Item
instance of: scholarly article
title: Generalized 2-symmetric submanifolds
zbMATH Open document ID: 0786.53033
DOI: 10.1007/BF01760008
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1993-05-16T00:00:00Z
review text: This paper is devoted to \({\overset {1} N}\)-symmetric submanifolds of Euclidean spaces, which are characterized as those having covariantly constant first normal map. (The locally symmetric submanifolds in the sense of D. Ferus form a special case). The main result is the characterization of all \({\overset {1} N}\)-symmetric submanifolds of Euclidean spaces which are totally geodesic submanifolds of direct products \(M\times \mathbb{R}^ d\), where \(M\) is a locally symmetric submanifold of some \(\mathbb{R}^ m\).
reviewed by: Oldřich Kowalski
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 169840
zbMATH Keywords: symmetric submanifolds
zbMATH Keywords: totally geodesic submanifolds
zbMATH Keywords: direct products
author: Antonella Carfagna D'Andrea
author: Giuliano Romani
MaRDI profile type: Publication
cites work: Normal and osculating maps for submanifolds of RN
cites work: Symmetric submanifolds of Euclidean space
cites work: Isometric imbeddings of compact symmetric spaces
cites work: Generalized symmetric submanifolds of Euclidean spaces
cites work: \(^{1}\)-symmetric submanifolds
cites work: k-symmetric submanifolds of \(R^ N\)
cites work: Q3881471
full work available at URL: https://doi.org/10.1007/bf01760008
OpenAlex ID: W2087303622
description: scientific article; zbMATH DE number 169840