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Geometry of real Grassmannian manifolds. I, II. (English. Russian original) Zbl 0918.53008
J. Math. Sci., New York 100, No. 3, 2239-2253 (2000); translation from Zalgaller, V. A. (ed.) et al., Geometry and topology. 2. Work collection. Sankt-Peterburg: Matematicheskij Institut Im. V. A. Steklova, Sankt-Peterburgskoe Otdelenie, RAN, Zap. Nauchn. Semin. POMI. 246, 84-107 (1997).
The author realizes the Plücker model of the real Grassmannian manifold as a submanifold of the Euclidean space \(\Lambda ({\mathbb R}^n)\) and establishes an isometry onto the classical Grassmannian manifold endowed with \(SO(n)\)-invariant metric. The decomposition of bi- and poly-vectors is studied.
[For Part III, see the following review Zbl 0918.53009)].

MSC:
53B25 Local submanifolds
15A75 Exterior algebra, Grassmann algebras
53A20 Projective differential geometry
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