Abstract
It is proved that faces of the unit spheres of the mass and comass norms are totally geodesic submanifolds in the manifolds of the extreme points of the spheres. A canonical embedding of the complex projective space \(\mathbb{C}P^{k-1}\) in the Plücker model of the Grassmannian \(G_2^+(\mathbb{R}^{2k}) \subset \Lambda^2 (\mathbb{R}^{2k})\) is described, and some of the properties of the embedding are proved. As an application of these results, the 2-dimensional sections in \(\mathbb{C}P^{k-1}\) having minimal curvature are characterized geometrically. Bibliography: 16 titles.
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Glushakov, A.N., Kozlov, S.E. Geodesics on Faces of Calibrations of Degree Two. Journal of Mathematical Sciences 110, 2783–2788 (2002). https://doi.org/10.1023/A:1015346127789
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DOI: https://doi.org/10.1023/A:1015346127789