Quaternionic submanifolds in quaternionic symmetric spaces
type: Item
instance of: scholarly article
title: Quaternionic submanifolds in quaternionic symmetric spaces
zbMATH Open document ID: 0593.53037
author: Hiroyuki Tasaki
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1986-01-01T00:00:00Z
review text: This paper is motivated by a theorem of the author [Tsukuba J. Math. 9, 117-131 (1985; Zbl 0581.53044)], which asserts that a compact quaternionic submanifold in a quaternionic Kähler manifold is homologically volume minimizing. Let M be a quaternionic symmetric space and \({\mathfrak g}\) the Lie algebra of the group of all isometries on M. The classification of quaternionic submanifolds in M is reduced to that of complex simple subalgebras of index 1 in \({\mathfrak g}^{{\mathbb{C}}}\). In the case that M is of classical type quaternionic submanifolds in M are completely classified by the use of the representation theory of complex simple Lie algebras. This classification enables us to investigate the homology classes represented by quaternionic submanifolds.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 3953745
zbMATH Keywords: quaternionic submanifold
zbMATH Keywords: quaternionic Kähler manifold
zbMATH Keywords: complex simple Lie algebras
zbMATH Keywords: quaternionic symmetric spaces
zbMATH Keywords: homologically value minimizing submanifolds
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228405
OpenAlex ID: W2010629523
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DOI: 10.2748/TMJ/1178228405
description: scientific article; zbMATH DE number 3953745