Geodesic
On the differential geometry of complexes of two-dimensional planes of the projective space $P^n$ containing a finite number of torsos and characterized by the configuration of their characteristic lines
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 2, Tome 221 (2023), pp. 31-41.

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This paper is devoted to the differential geometry of complexes of two-dimensional planes in the projective space $P^n$ containing a finite number of torsos. We find a necessary condition under which the complex $C^\rho$ contains a finite number of torsos, examine the properties of complexes of two-dimensional planes, which are determined by a special configuration of characteristic straight torsos belonging to the complex, and establish the structure and conditions for the existence of such complexes. The self-duality of such complexes is determined.
Keywords: Grassmann manifold, complex of multidimensional planes, Segre manifold. 
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I. V. Bubyakin. On the differential geometry of complexes of two-dimensional planes of the projective space $P^n$ containing a finite number of torsos and characterized by the configuration of their characteristic lines. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 2, Tome 221 (2023), pp. 31-41. http://geodesic.mathdoc.fr/item/INTO_2023_221_a3/

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