Calibrated geometries in quaternionic Grassmannians
type: Item
instance of: scholarly article
title: Calibrated geometries in quaternionic Grassmannians
zbMATH Open document ID: 0704.53055
author: Hiroyuki Tasaki
published in: Osaka Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The method of calibrated geometries is applied to the invariant differential forms on the quaternionic Grassmannians \(G_ p({\mathbb{H}}^{p+q})\) of p-dimensional right \({\mathbb{H}}\)-subspaces of the \(p+q\)-dimensional right quaternionic vector space \({\mathbb{H}}^{p+1}\) to show that the sub-Grassmannians \(G_ p(E)\) of p-dimensional right \({\mathbb{H}}\)-subspaces of a \(p+r\)-dimensional right \({\mathbb{H}}\)-subspace E of \({\mathbb{H}}^{p+q}\) are volume minimizing in their real homology classes. Moreover, it is shown that any volume minimizing submanifold in such homology classes are congruent to a sub-Grassmannian.
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 4155389
zbMATH Keywords: calibrated geometries
zbMATH Keywords: quaternionic Grassmannians
zbMATH Keywords: volume minimizing
zbMATH Keywords: homology classes
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4155389