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 Tr. Mat. Inst. Steklova, 1999, Volume 224, Pages 56–67 (Mi tm691)

This article is cited in 5 scientific papers (total in 6 papers)

Relatives of the Quotient of the Complex Projective Plane by the Complex Conjugation

V. I. Arnol'd

Abstract: It is proved that the quotient space of the four-dimensional quaternionic projective space by the automorphism group of the quaternionic algebra becomes the 13-dimensional sphere while quotioned by the quaternionic conjugation. This fact and its various generalizations are proved using the results of the theory of the hyperbolic partial differential equations, providing also the proof of the theorem (which was, it seems, known to L. S. Pontriagin in the 1930s) claiming that the quotient of the complex projective plane by the complex conjugation is the 4-sphere.

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English version:
Proceedings of the Steklov Institute of Mathematics, 1999, 224, 46–56

Bibliographic databases:
UDC: 515.1+512
Received in September 1998

Citation: V. I. Arnol'd, “Relatives of the Quotient of the Complex Projective Plane by the Complex Conjugation”, Algebra. Topology. Differential equations and their applications, Collection of papers dedicated to the 90th anniversary of academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 224, Nauka, MAIK «Nauka/Inteperiodika», M., 1999, 56–67; Proc. Steklov Inst. Math., 224 (1999), 46–56

Citation in format AMSBIB
\Bibitem{Arn99} \by V.~I.~Arnol'd \paper Relatives of the Quotient of the Complex Projective Plane by the Complex Conjugation \inbook Algebra. Topology. Differential equations and their applications \bookinfo Collection of papers dedicated to the 90th anniversary of academician Lev Semenovich Pontryagin \serial Tr. Mat. Inst. Steklova \yr 1999 \vol 224 \pages 56--67 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm691} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1721354} \zmath{https://zbmath.org/?q=an:0963.53023} \transl \jour Proc. Steklov Inst. Math. \yr 1999 \vol 224 \pages 46--56 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. I. Arnol'd, “Lagrangian Grassmannian of a Quaternion Hypersymplectic Space”, Funct. Anal. Appl., 35:1 (2001), 61–63
2. V. A. Vassiliev, “Spaces of Hermitian operators with simple spectra and their finite-order cohomology”, Mosc. Math. J., 3:3 (2003), 1145–1165
3. E. Straume, “A geometric study of many body systems”, Lobachevskii J. Math., 24 (2006), 73–134
4. “Vladimir Igorevich Arnol'd (on his 70th birthday)”, Russian Math. Surveys, 62:5 (2007), 1021–1030
5. Gambioli A., Nagatomo Y., Salamon S., “Special Geometries Associated To Quaternion-Kahler 8-Manifolds”, J. Geom. Phys., 91 (2015), 146–162
6. Kanjamapornkul K., Pincak R., “Kolmogorov space in time series data”, Math. Meth. Appl. Sci., 39:15 (2016), 4463–4483
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