Isometric reflections with respect to submanifolds and the Ricci operator of geodesic spheres
type: Item
instance of: scholarly article
title: Isometric reflections with respect to submanifolds and the Ricci operator of geodesic spheres
zbMATH Open document ID: 0712.53023
DOI: 10.1007/BF01308672
author: Philippe Tondeur
author: Lieven Vanhecke
published in: Monatshefte für Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178446
review text: Let B be a submanifold of a Riemannian manifold (M,g), and \(\phi_ B\) the reflection with respect to B, reversing geodesics orthogonal to B on a sufficiently small tubular neighborhood. We derive a characterization of the property that \(\phi_ B\) is isometric by means of the Ricci operator on geodesic spheres tangent to B.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4171879
zbMATH Keywords: submanifold
zbMATH Keywords: reflection
zbMATH Keywords: geodesics
zbMATH Keywords: Ricci operator
reviewed by: Lieven Vanhecke
MaRDI profile type: Publication
cites work: Q4169382
cites work: Q5678153
cites work: Differential geometry of geodesic spheres.
cites work: Q3982336
cites work: Symmetries and locally s-regular manifolds
cites work: Q3031557
description: scientific article; zbMATH DE number 4171879