Abstract
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 constructivemethod yielding the canonical (= simplest) decomposition is presented. Bibliography: 8 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 147–158.
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Nikanorova, M.Y. Canonical representation of tangent vectors of Grassmannians. J Math Sci 140, 582–588 (2007). https://doi.org/10.1007/s10958-007-0440-7
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DOI: https://doi.org/10.1007/s10958-007-0440-7