Characterization of totally geodesic Kähler immersions
type: Item
instance of: scholarly article
title: Characterization of totally geodesic Kähler immersions
zbMATH Open document ID: 1028.53017
author: Kaoru Suizu
author: Sadahiro Maeda
author: Toshiaki Adachi
published in: Hokkaido Mathematical Journal
publication date: 2004-01-22T00:00:00Z
review text: In his paper [Nagoya Math. J. 60, 180-188 (1976; Zbl 0305.53046)], \textit{K. Nomizu} characterized totally geodesic complex projective spaces among Kähler submanifolds of a complex projective space using an extrinsic property of geodesics. The introduction of the paper presents a review of results on the characterization of submanifolds by the extrinsic shape of some families of curves in the submanifold. The authors characterize totally geodesic Kähler submanifolds of an arbitrary Kähler manifold by the extrinsic shape (in the manifold) of trajectories of a Kähler magnetic field on the submanifold. Then using the same technique they characterize planar geodesic immersions of the Cayley projective plane \(CaP^2\) into a real space form.
reviewed by: Robert A. Wolak
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1876752
zbMATH Keywords: Kähler immersion
zbMATH Keywords: submanifold
zbMATH Keywords: totally geodesic
zbMATH Keywords: Cayley projective plane
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1350911905
OpenAlex ID: W2007686045
Wikidata QID: Q125618866
DOI: 10.14492/HOKMJ/1350911905
description: scientific article; zbMATH DE number 1876752