zbMATH — the first resource for mathematics

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.
53C35 Differential geometry of symmetric spaces
15A75 Exterior algebra, Grassmann algebras
Full Text: DOI Link EuDML
[1] S. E. Kozlov, ”Geometry of real Grassmann manifolds. I, II,” Zap. Nauchn. Semin. POMI, 246, 84–107 (1997). · Zbl 0918.53008
[2] S. E. Kozlov, ”Geometry of real Grassmann manifolds. III,” Zap. Nauchn. Semin. POMI, 246, 108–129 (1997). · Zbl 0918.53009
[3] A. A. Borisenko and Yu. N. Nikolaevskii, ”Grassmann manifolds and Grassmann image of manifolds,” Uspekhi Mat. Nauk, 46, No. 2, 41–81 (1991).
[4] E. Cartan, Oeuvres Completes. I, Paris (1952).
[5] K. Leichtweiss, ”Zur Riemannschen Geometrie in Grassmannschen Mannigfaltigkeiten,” Math. Z., 76, 334–366 (1961). · Zbl 0113.37102
[6] S. E. Kozlov, ”Orthogonally invariant Riemannian metrics on real Grassmann manifolds,” Mat. Fiz. Analiz. Geometr., 4, Nos. 1–2 (1997). · Zbl 0967.53034
[7] F. R. Gantmakher, Matrix Theory [in Russian], Moscow (1966).
[8] S. E. Kozlov, ”Geometry of real Grassmann manifolds. V,” Zap. Nauchn. Semin. POMI, 252, 104–120 (1998).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.