Harmonic mappings, minimal and totally geodesic immersions of compact Riemannian homogeneous spaces into Grassmann manifolds
type: Item
instance of: scholarly article
title: Harmonic mappings, minimal and totally geodesic immersions of compact Riemannian homogeneous spaces into Grassmann manifolds
zbMATH Open document ID: 0810.53049
author: Osamu Ikawa
published in: Kodai Mathematical Journal
publication date: 1995-04-09T00:00:00Z
review text: Let \(M\) and \(N\) be two compact connected Riemannian manifolds. A smooth mapping \(F : M \to N\) is called harmonic if it is an extremal of the energy. Moreover, if the harmonic mapping \(F : M \to N\) is an isometric immersion, then \(F\) is a minimal immersion. An isometric immersion \(F : M \to N\) is called totally geodesic if \(F\) carries every geodesic of \(M\) to a geodesic of \(N\). A totally geodesic immersion is especially minimal. The existence and construction of minimal immersions and harmonic mappings are interesting and important problems in various situations. In the previous paper [Tsukuba J. Math. 17, No. 1, 169-188 (1993)], we constructed harmonic mappings and minimal immersions from compact Riemannian homogeneous spaces into Grassmann manifolds. In this paper, we study a different construction of harmonic mappings, minimal and totally geodesic immersions of compact Riemannian homogeneous spaces into Grassmann manifolds.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 515599
zbMATH Keywords: harmonic mapping
zbMATH Keywords: minimal immersion
zbMATH Keywords: totally geodesic immersion
Wikidata QID: Q115224582
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039791
OpenAlex ID: W2107252990
cites work: Equivariant minimal immersions of compact Riemannian homogeneous spaces into compact Riemannian homogeneous spaces
cites work: Minimal immersions of Riemannian manifolds
cites work: Q5640359
DOI: 10.2996/KMJ/1138039791
description: scientific article; zbMATH DE number 515599