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Projective space; the Grassmann manifold; principal fiber bundle; Neifeld’s connection
The work concerns to investigations in the field of differential geometry. It is realized by a method of continuations and scopes of G. F. Laptev which generalizes a moving frame method and Cartan’s exterior forms method and depends on calculation of exterior differential forms. The Grassmann manifold (space of all $m$-planes) is considered in the $n$-dimensional projective space $P_n$. Principal fiber bundle of tangent linear frames is arised above this manifold. Typical fiber of the principal fiber bundle is the linear group working in the tangent space to the Grassmann manifold. Neifeld’s connection is given in this fibering. It is proved by Cartan’s external forms method, that Bortolotti’s clothing of the Grassmann manifold induces this connection.
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[3] Bortolotti, E.: Connessioni nelle varieta luogo di spazi. Rend. Semin. Fac. Sci. Univ. Cagliari 3 (1933), 81–89. Zbl 0007.36604
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