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Статья
2018

Geometric Construction of Linear Complex of Planes of B3 Type


A. N. MakokhaA. N. Makokha
Русская математика
https://doi.org/10.3103/S1066369X18110026
Abstract / Full Text

Using invariant geometric images of a trivector of the type (884; 400), we construct its basic group of automorphisms. We formulate and prove a theorem on necessary and sufficient conditions for determining all planes of a linear complex associated with a trivector of the given type up to linear transformations of its automorphism group. Proving the theorem, we find all kinds of singular lines and construct the polar hyperplanes for nonsingular lines.

Author information
  • North-Caucasian Federal University, ul. Pushkina 1, Stavropol, 355009, RussiaA. N. Makokha
References
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  2. Longo, C. “Sui Complessi Lineari di Piani”, Ann. Mat. Pura Appl.. 37, 61–138 (1954).
  3. Gurevich, G. B. “Algebra of a Trivector”. II, Trans. of Semin. On Vector and Tensor Analysis 6, 28–124 (Moscow State University, 1948) [in Russian].
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  5. Makokha, A. N. “Automorphism Groups of Trivectors of Rank Eight”, Trans. of Int. Geom. Workshop Dedicated to N. V. Efimov (Ed. by S. B. Klimentov), Abrau–Dyurso, September 27–October 4, 1996 (NPP KORALL–MIKRO, Rostov–on–Don, 1996), pp. 50–51 [in Russian].
  6. Makokha, A.N. “LinearOperators Connected with a Trivector of Type (887; 520) and the BasicAutomorphism Group of That Trivector”, Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 46–53 (1981).[in Russian].
  7. Makokha, A. N. “A Group of Automorphisms of a Linear Complex of Planes of Type A3 and the Singular Straight Lines of This Complex”, Sov.Math. 30, No. 8, 52–59 (1986).
  8. Makokha, A. N. “The Group of Linear Transformations Preserving a Trivector of Type (888; 852)”, Sov. Math. 32, No. 2, 63–67 (1988).
  9. Makokha, A. N. “Properties of Linear Operators Connected with a Trivector of Type B3”, Vestn. Stavropol Gos. Univ., No. 7, 33–36 (1996).[in Russian].