Literature Cited
S. L. Pevzner, “Automorphisms of pairs of quadrics in projective space. I,” Sibirsk. Matem. Zh.,7, No.5, 1076–1086 (1966).
S. L. Pevzner, “Automorphisms of paris of quadrics in projective space. II,” Sibirsk. Matem. Zh.,8, No. 6, 1385–1398 (1967).
S. L. Pevzner, “Geometry of pairs of quadrics in projective space,” Sibirsk Matem. Zh.,10, 116–134 (1969).
S. L. Pevzner, “Automorphisms of quadrics in non-Euclidean space representable by motions in plural non-Euclidean spaces,” Izv. Vuzov (Matem.),9, 69–77 (1968).
A. I. Mal'tsev, Fundamentals of Linear Algebra [in Russian], GITTL, Moscow (1955).
I. M. Yaglom, “Square and skewsymmetric, bilinear forms in real symplectic spaces” Tr. Seminara po Vektorn. i Tensorn. Analizu pri MGU,8, 364–381 (1950).
Yu. B. Ermolaev, “Simultaneous reduction of pairs of bilinear forms to canonical form,” Dokl. Akad. Nauk SSSR,132, No. 2, 257–259 (1960).
L. S. Pontryagin, Continuous. Groups [in Russian], GITTL, Moscow (1954).
R. L. Bishop and R. J. Crittenden, Geometry of Manifolds, Academic Press, New York (1964).
K. Schroder, “Uber k-parametrigen Matrizengruppen,” Deutsche Math.,4, No. 2, 201–225 (1939).
B. A. Rozenfel'd and A. A. Abramov, “Space of affine connectivity and symmetric space,” Uspekhi Matm. Nauk,6, No. 2, 72–147 (1950).
E. B. Dynkin, “On the representation of the series log(exey) of noncommuting x and y in terms of commutators,” Matem. Sb.,25, No. 1, 155–162 (1949).
L. N. Kuznetsova, “Automorphism of pairs of null systems in complex projective space,”. in: Third Intercollegiate Scientific Conference on Problems of Geometry (abstracts) [in Russian], Kazan (1967), p. 88.
B. A. Rozenfel'd, Non-Euclidean Space [in Russian], Nauka, Moscow (1969).
L. P. Andreeva and L. V. Shestyreva, “Limiting symplectic spaces,” in: Projective Metrics [in Russian], Uch. Zapiski Kolomensk. Ped. In-ta,8, 23–44 (1965).
Lo-gen Khua and B. A. Rozenfel'd, “The geometry of rectangular matrices and its application to real projective and non-Euclidean geometries,” Izv. Vuzov. (Matem.),1, 233–247 (1957).
B. A. Rozenfel'd, “Rectangular matrices and non-Euclidean geometries,” Uspekhi Matem. Nauk,13, No. 6, 21–48 (1958).
V. V. Vishnevskii, “On one class of spaces over plural algebras,” Vyzov. (Matem.),2, 14–22 (1969).
K. Teleman, Elements of Topology and Differentiable Manifolds [Russian translation], Mir, Moscow (1967).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 12, No.2, pp. 397–413, March–April, 1971.
Rights and permissions
About this article
Cite this article
Pevzner, S.L. Automorphism groups of quadrics and null systems in non-euclidean symplectic spaces and the geometry of these groups. Sib Math J 12, 281–293 (1971). https://doi.org/10.1007/BF00969050
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00969050