Geodesic
About the structure of complexes of $m$-dimensional planes in projective space $P^n$ containing a finite number of developable surfaces
Matematičeskie zametki SVFU, Tome 24 (2017), pp. 3-16

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We consider the projective differential geometry of $m$-dimensional plane submanifolds of manifolds $G(m, n)$ in projective space $P^n$ containing a finite number of developable surfaces. To study such submanifolds we use the Grassmann mapping of manifolds $G(m, n)$ of $m$-dimensional planes in projective space $P^n$ to $(m + 1)(n-m)$-dimensional algebraic manifold $\Omega(m, n)$ of space $P^N$, where $N=\left(\begin{array}{c}m+1\\n+1\\\end{array}\right)-1$. This mapping combined with the method of external Cartan's forms and moving frame method made it possible to determine the dependence of considered manifolds structure and the configuration of the $(m - 1)$-dimensional characteristic planes and $(m + 1)$-dimensional tangential planes of developable surfaces that belong to considered manifolds.
Keywords: Grassmann manifold, complexes of multidimensional planes, Grassmann mapping, Segre manifold. 
@article{SVFU_2017_24_a0,
     author = {I. V. Bubyakin},
     title = {About the structure of complexes of $m$-dimensional planes in projective space $P^n$ containing a finite number of developable surfaces},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {3--16},
     publisher = {mathdoc},
     volume = {24},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2017_24_a0/}
}
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I. V. Bubyakin. About the structure of complexes of $m$-dimensional planes in projective space $P^n$ containing a finite number of developable surfaces. Matematičeskie zametki SVFU, Tome 24 (2017), pp. 3-16. http://geodesic.mathdoc.fr/item/SVFU_2017_24_a0/