Congruence theorems for point triples in Grassmann manifolds \(G_2(\mathbb{R}^N)\) (Q1373410)

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 \(N = 4,5,6\).