Eigenmaps and minimal immersions of projective spaces into spheres
type: Item
instance of: scholarly article
title: Eigenmaps and minimal immersions of projective spaces into spheres
zbMATH Open document ID: 0648.53033
author: Katsuya Mashimo
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1988-01-01T00:00:00Z
review text: In [Ann. Math., II. Ser. 93, 43-62 (1971; Zbl 0218.53069)] \textit{M. P. do Carmo} and \textit{N. R. Wallach} showed that the set of equivalence classes of full isometric minimal immersions of a compact symmetric space M into a sphere can be parameterized by a convex body in a vector space \(L_ M\). Similarly, \textit{G. Toth} and \textit{G. d'Ambra} showed in [Geom. Dedicata 17, 61-67 (1984; Zbl 0551.58013)] that equivalence classes of full eigenmaps of M into a sphere can be parameterized by a convex body in a vector space \(L_ E\). The author estimates the dimension of \(L_ M\) and \(L_ E\) from below when M is a quaternionic projective space or the Cayley plane. This was done for complex projective spaces by \textit{H. Urakawa} in [Tsukuba J. Math. 9, 321-347 (1985; Zbl 0588.53041)].
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 4058352
zbMATH Keywords: minimal immersions
zbMATH Keywords: symmetric space
zbMATH Keywords: quaternionic projective space
zbMATH Keywords: Cayley plane
reviewed by: Gudlaugur Thorbergsson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228029
OpenAlex ID: W2046136281
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DOI: 10.2748/TMJ/1178228029
description: scientific article; zbMATH DE number 4058352