RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 1991, Volume 182, Number 2, Pages 203–219 (Mi msb1292)  

This article is cited in 36 scientific papers (total in 36 papers)

On holomorphic transformations of a quadric

V. K. Beloshapka


Abstract: Holomorphic transformations of a quadric of arbitrary codimension are studied. General formulas are derived for infinitesimal automorphisms of such a surface. The phenomenon of “rigidity” of quadrics in general position is demonstrated. Examples of quadrics with rich automorphism groups are considered. A classification is given for positive-definite quadrics of codimension two.

Full text: PDF file (1744 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1992, 72:1, 189–205

Bibliographic databases:

UDC: 517.5
MSC: Primary 32M05, 32H99; Secondary 32C05, 14J25
Received: 01.11.1989

Citation: V. K. Beloshapka, “On holomorphic transformations of a quadric”, Mat. Sb., 182:2 (1991), 203–219; Math. USSR-Sb., 72:1 (1992), 189–205

Citation in format AMSBIB
\Bibitem{Bel91}
\by V.~K.~Beloshapka
\paper On holomorphic transformations of a~quadric
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 2
\pages 203--219
\mathnet{http://mi.mathnet.ru/msb1292}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1103272}
\zmath{https://zbmath.org/?q=an:0728.32011}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992SbMat..72..189B}
\transl
\jour Math. USSR-Sb.
\yr 1992
\vol 72
\issue 1
\pages 189--205
\crossref{https://doi.org/10.1070/SM1992v072n01ABEH001267}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992JF72300011}


Linking options:
  • http://mi.mathnet.ru/eng/msb1292
  • http://mi.mathnet.ru/eng/msb/v182/i2/p203

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. E. M. Chirka, “Introduction to the geometry of $CR$-manifolds”, Russian Math. Surveys, 46:1 (1991), 95–197  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. V. Abrosimov, “A description of locally biholomorphic automorphisms of standard quadrics of codimension two”, Russian Acad. Sci. Sb. Math., 80:1 (1995), 137–178  mathnet  crossref  mathscinet  zmath  isi
    3. Vladimir V. Ežov, Gerd Schmalz, “Holomorphic automorphisms of quadrics”, Math Z, 216:1 (1994), 453  crossref  mathscinet  zmath  isi
    4. Vladimir V. Ežov, Gerd Schmalz, “Poincaré automorphisms for nondegenerate CR quadrics”, Math Ann, 298:1 (1994), 79  crossref  mathscinet  zmath  isi
    5. V. K. Beloshapka, “Geometric invariants of a $CR$-manifold”, Math. Notes, 55:5 (1994), 439–445  mathnet  crossref  mathscinet  zmath  isi
    6. N. F. Palinchak, “On quadrics of higher codimension”, Math. Notes, 55:5 (1994), 512–516  mathnet  crossref  mathscinet  zmath  isi
    7. N. F. Palinchak, “Real quadrics of codimension 3 in $\mathbb C^6$ and their non-linear automorphisms”, Izv. Math., 59:3 (1995), 597–617  mathnet  crossref  mathscinet  zmath  isi
    8. V. K. Beloshapka, “Invariants of CR-manifolds associated with the tangent quadric”, Math. Notes, 59:1 (1996), 31–38  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. A. F. Arbatskii, “Structure of groups of nonlinear automorphisms for $(3,3)$ quadrics”, Math. Notes, 59:2 (1996), 116–122  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. N. F. Palinchak, “About $c$-rigid quadrics”, Math. Notes, 59:2 (1996), 158–162  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. V. K. Beloshapka, “Local invariants and prohibitions on mappings of CR-manifolds”, Math. Notes, 60:4 (1996), 438–441  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. V. K. Beloshapka, “Homogeneous real hypersurfaces in $\mathbb C^2$”, Math. Notes, 60:5 (1996), 569–572  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. Beloshapka V., “Automorphisms of Degenerate Hypersurfaces in C-2 and a Dimension Conjecture”, Russ. J. Math. Phys., 4:3 (1996), 393–396  mathscinet  zmath  isi
    14. V. V. Ezhov, G. Schmalz, “A simple proof of the Beloshapka theorem on the parametrization of the automorphism group of a CR manifold”, Math. Notes, 61:6 (1997), 783–786  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. E. G. Anisova, “Null-quadrics of codimension 4 in $\mathbb C^7$”, Math. Notes, 62:5 (1997), 549–556  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. Beloshapka V., “Cr-Varieties of the Type (1,2) as Varieties of “Super-High” Codimension”, Russ. J. Math. Phys., 5:3 (1997), 399–404  mathscinet  zmath  isi
    17. V. V. Ezov, G. Schmalz, “Automorphisms and holomorphic mappings of standard CR-manifolds and Siegel domains”, Journal of Mathematical Sciences (New York), 92:2 (1998), 3712  crossref  mathscinet  zmath
    18. E. G. Anisova, “Quadrics of codimension 4 in $\mathbb C^7$ and their automorphisms”, Math. Notes, 64:6 (1998), 697–703  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. Vladimir V. Ežov, Gerd Schmalz, “A Matrix Poincaré formula for holomorphic automorphisms of quadrics of higher codimension. Real Associative Quadrics”, J Geom Anal, 8:1 (1998), 27  crossref
    20. V. V. EZHOV, A. V. ISAEV, G. SCHMALZ, “INVARIANTS OF ELLIPTIC AND HYPERBOLIC CR-STRUCTURES OF CODIMENSION 2”, Int. J. Math, 10:01 (1999), 1  crossref
    21. E. N. Shananina, “Models of CR-manifolds of type $(\ell,K)$ for $3\leqslant K\leqslant 7$ and their automorphisms”, Math. Notes, 67:3 (2000), 382–388  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    22. Baouendi M., Ebenfelt P., Rothschild L., “Local Geometric Properties of Real Submanifolds in Complex Space”, Bull. Amer. Math. Soc., 37:3 (2000), 309–336  crossref  mathscinet  zmath  isi
    23. V. K. Beloshapka, “A Cubic Model of a Real Variety”, Math. Notes, 70:4 (2001), 457–470  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    24. A. E. Ershova, “Automorphisms of 2-Nondegenerate Hypersurfaces in $\mathbb C^3$”, Math. Notes, 69:2 (2001), 188–195  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    25. V. K. Beloshapka, “Polynomial models of real manifolds”, Izv. Math., 65:4 (2001), 641–657  mathnet  crossref  crossref  mathscinet  zmath  elib
    26. V. K. Beloshapka, “A Quasiperiodic System of Polynomial Models of CR-Manifolds”, Proc. Steklov Inst. Math., 235 (2001), 1–28  mathnet  mathscinet  zmath
    27. V. K. Beloshapka, “Real submanifolds in complex space: polynomial models, automorphisms, and classification problems”, Russian Math. Surveys, 57:1 (2002), 1–41  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    28. P. B. Utkin, “The Dimension Conjecture for Quadrics of Codimension Three and Higher”, Math. Notes, 72:1 (2002), 138–141  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    29. A. B. Sukhov, “On transformations of analytic CR-structures”, Izv. Math., 67:2 (2003), 303–332  mathnet  crossref  crossref  mathscinet  zmath  isi
    30. V. K. Beloshapka, “Universal Models For Real Submanifolds”, Math. Notes, 75:4 (2004), 475–488  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    31. E. N. Shananina, “Polynomial Models of Degree 5 and Algebras of Their Automorphisms”, Math. Notes, 75:5 (2004), 702–716  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    32. Gaussier H., Merker J., “Nonalgebraizable Real Analytic Tubes in C-N”, Math. Z., 247:2 (2004), 337–383  crossref  mathscinet  zmath  isi
    33. Wilhelm Kaup, “CR-quadrics with a symmetry property”, manuscripta math, 2010  crossref
    34. Wu Q., “On Holomorphic Automorphisms of a Class of Non-Homogeneous Rigid Hypersurfaces in a", (N+1)”, Chin. Ann. Math. Ser. B, 31:2 (2010), 201–210  crossref  mathscinet  zmath  isi
    35. Isaev A., “Spherical Tube Hypersurfaces”, Spherical Tube Hypersurfaces, Lect. Notes Math., 2020, Springer-Verlag Berlin, 2011, 1–217  crossref  mathscinet  isi  elib
    36. I. B. Mamai, “Moduli spaces of model surfaces with one-dimensional complex tangent”, Izv. Math., 77:2 (2013), 354–377  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник - 1991 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:339
    Full text:88
    References:24
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019