Geodesic
Differentiable mappings of affine spaces into manifolds of $m$-planes in a~multidimensional Euclidean space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2009), pp. 24-42

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In this paper we consider a differentiable mapping of a $p$-dimensional affine space into the differentiable manifold $\mathfrak M_N$ of all centered $m$-planes in the $n$-dimensional Euclidean space. We pay the special attention to describing geometric images defined by the fundamental geometric object of a certain mapping.
Keywords: Euclidean space, differentiable manifold, differentiable mapping, fundamental geometric object.
Mots-clés : affine space, Cauchy–Riemann conditions 
@article{IVM_2009_11_a3,
     author = {E. T. Ivlev and E. A. Moldovanova},
     title = {Differentiable mappings of affine spaces into manifolds of $m$-planes in a~multidimensional {Euclidean} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {24--42},
     publisher = {mathdoc},
     number = {11},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_11_a3/}
}
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E. T. Ivlev; E. A. Moldovanova. Differentiable mappings of affine spaces into manifolds of $m$-planes in a~multidimensional Euclidean space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2009), pp. 24-42. http://geodesic.mathdoc.fr/item/IVM_2009_11_a3/