Congruence theorems for point triples in Grassmann manifolds \(G_2(\mathbb{R}^N)\)
type: Item
instance of: scholarly article
title: Congruence theorems for point triples in Grassmann manifolds \(G_2(\mathbb{R}^N)\)
zbMATH Open document ID: 0897.53038
DOI: 10.1007/BF02844509
author: Giovanni Masala
publication date: 1998-09-28T00:00:00Z
review text: The problem of congruence for triangles in the Grassmann manifold \(G_2(\mathbb{R}^N)\) of 2-planes in \(\mathbb{R}^N\) is studied. It suffices to assume that \(N\leq 6\), the case \(N = 3\) being well known. Replacing any point of \(G_2(\mathbb{R}^N)\) by the corresponding orthogonal projector, one reduces the problem to classical invariant theory of matrices. Using the canonical form of a triple of points in \(G_2(\mathbb{R}^N)\) established by \textit{T. Hangan} [Rend. Semin. Mat., Torino 50, 367-380 (1992; Zbl 0805.53047)], the author lists the invariants determining the isometry class of a triple for \(N = 4,5,6\).
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 15A72
zbMATH DE Number: 1089781
zbMATH Keywords: Grassmann manifold
zbMATH Keywords: isometric triples
zbMATH Keywords: critical angles
zbMATH Keywords: invariants of matrices
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02844509
OpenAlex ID: W2030922205
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1089781