Isometric immersions with geodesic normal sections in semi-Riemannian geometry
type: Item
instance of: scholarly article
title: Isometric immersions with geodesic normal sections in semi-Riemannian geometry
zbMATH Open document ID: 1171.53038
author: Kouhei Miura
published in: Tokyo Journal of Mathematics
publication date: 2009-04-21T00:00:00Z
review text: Let \(\tilde{M}\) be a Riemannian space form and \(f:M\rightarrow \tilde{M}\) an isometric immersion with geodesic normal section. It is known that in Riemannian geometry all geodesics of \(M\) have the same proper order in \(\tilde{M}\). However this does not hold when \(\tilde{M}\) is an indefinite semi-Riemannian manifold. In this paper, the authors proves sufficient conditions for an isometric immersion with geodesic normal to be helical.
reviewed by: Constantin Călin
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 5545424
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1233844064
OpenAlex ID: W1996636147
Wikidata QID: Q115219852
cites work: Q4169382
cites work: Planar geodesic immersions in pseudo-Euclidean space
cites work: Submanifolds with geodesic normal sections
cites work: Higher Curvatures of Curves in Euclidean Space
cites work: Helical immersions and normal sections
cites work: Minimal surfaces of pseudo-Euclidean spaces with geodesic normal sections
cites work: Helical geodesic immersions of semi-Riemannian manifolds
cites work: Construction of harmonic maps between semi-Riemannian spheres
cites work: Helical immersions into a unit sphere
cites work: Q4720352
DOI: 10.3836/TJM/1233844064
description: scientific article; zbMATH DE number 5545424