Riemannian submersion with isometric reflections with respect to the fibers
type: Item
instance of: scholarly article
title: Riemannian submersion with isometric reflections with respect to the fibers
zbMATH Open document ID: 0795.53042
published in: Kodai Mathematical Journal
publication date: 1994-09-26T00:00:00Z
review text: A Riemannian submersion \(\pi:M \to N\) generates a family of local reflections w.r.t. the fibers. These are local geodesic symmetries for horizontal geodesics. A Sasakian structure \((\varphi,V,\eta)\) on a Riemannian manifold \(M\) is \(\varphi\)-symmetric when \(\varphi^ 2 ((\nabla_ XR) (Y,Z)H)=0\) for all \(X,Y,Z\) and all \(H\) orthogonal to \(V\). The author proves that, under some additional assumptions on the integrability tensor \(A\) of \(\pi\), the reflections w.r.t. the fibers are isometries iff \(M\) admits a Sasakian \(\varphi\)-symmetric structure.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 558887
zbMATH Keywords: \(\varphi\)-symmetric structure
zbMATH Keywords: Riemannian submersion
zbMATH Keywords: geodesic symmetries
zbMATH Keywords: Sasakian structure
author: Fumio Narita
reviewed by: Paweł Walczak
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039849
OpenAlex ID: W2071972475
Wikidata QID: Q115224580
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DOI: 10.2996/KMJ/1138039849
description: scientific article; zbMATH DE number 558887