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Canonical representation of tangent vectors of Grassmannians. (English. Russian original) Zbl 1151.53340
J. Math. Sci., New York 140, No. 4, 582-588 (2007); translation from Zap. Nauchn. Semin. POMI 329, 147-158 (2005).
Summary: The structure of the tangent bundle of the real Grassmann manifold \(G_+^{p,n}\) under the Plücker embedding (in the exterior algebra of the initial Euclidean space) is studied. Explicit expressions for the relation between decompositions of a tangent vector with respect to different bases of the tangent space are obtained, and a constructive method yielding the canonical (= simplest) decomposition is presented.
MSC:
53C35 Differential geometry of symmetric spaces
15A75 Exterior algebra, Grassmann algebras
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References:
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