Geodesic
Neifeld’s Connection Inducedon the Grassmann Manifold
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 1, pp. 11-14 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 53A20, 53B25
Keywords: Projective space; the Grassmann manifold; principal fiber bundle; Neifeld’s connection 
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Belova, Olga. Neifeld’s Connection Inducedon the Grassmann Manifold. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 1, pp. 11-14. http://geodesic.mathdoc.fr/item/AUPO_2016_55_1_a1/

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