Browse > Article
http://dx.doi.org/10.4134/JKMS.2003.40.3.391

ROTATIONALLY INVARIANT COMPLEX MANIFOLDS  

Isaev, A.V. (Department of Mathematics The Australian National University)
Publication Information
Journal of the Korean Mathematical Society / v.40, no.3, 2003 , pp. 391-408 More about this Journal
Abstract
In this paper we discuss complex manifolds of dimension $n{\ge}2$ that admit effective actions of either $U_n$\;or\;$SU_n$ by biholomorphic transformations.
Keywords
complex manifolds; group actions;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 H. Rossi, Attaching analytic spaces to an analytic space along a pseudoconcave boundary, Proc. Conf. Complex Analysis, Minneapolis, 1964, Springer-Verlag,1965, 242-256.
2 H. Rossi, Homogeneous strongly pseudoconvex hypersurfaces, Proc. Conf. Complex Analysis Rice Univ., Houston, 1972, Rice Univ. Studies, 59 (1973), no. 1, 131-145.
3 F. Uchida, Smooth actions of special unitary groups on cohomology complex projective spaces, Osaka J. Math. 12 (1975), 375-400.
4 E. Vinberg and A. Onishchik, Lie Groups and Algebraic Groups, Springer-Verlag, 1990.
5 J. A. Gifford, A. V. Isaev and S. G. Krantz, On the dimensions of the auto-morphism groups of hyperbolic Reinhardt domains, Illinois J. Math. 44 (2000), 602–618.
6 R. E. Greene and S. G. Krantz, Characterization of complex manifolds by the isotropy subgroups of their automorphism groups, Indiana Univ. Math. J. 34 (1985), 865–879.   DOI
7 W. Y. Hsiang, On the principal orbit type and P. A. Smith theory of SU(p) actions, Topology 6 (1967), 125–135.   DOI   ScienceOn
8 D. Barrett, E. Bedford and J. Dadok, $\mathbb{T}^n-actions $ on holomorphically separable complex manifolds, Math. Z. 202 (1989), 65–82.   DOI
9 J. Bland, T. Duchamp and M. Kalka, A characterization of $\mathbb{CP}^n$ by its automor-phism group, Complex Analysis (University Park, Pa, 1986), 60–65, Lecture Notes In Mathematics 1268, Springer-Verlag, 1987.   DOI
10 W. C. Hsiang and W. Y. Hsiang, Some results on differentiable actions, Bull. Amer. Math. Soc. 72 (1966), 134–138.   DOI
11 A. V. Isaev and S. G. Krantz, On the automorphism groups of hyperbolic manifolds, J. Reine Angew. Math. 534 (2001), 187-194.   DOI
12 A. V. Isaev and N. G. Kruzhilin, Effective actions of the unitary group on complex manifolds, to appear in Canad. J. Math. in 2002
13 W. Kaup, Reelle Transformationsgruppen und invariante Metriken auf komplexen Räumen, Invent. Math. 3 (1967), 43-70.   DOI
14 A. Kruger, Homogeneous Cauchy-Riemann structures, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1991), no. 4, 193-212.
15 A. Klimyk and K. Schmudgen, Quantum groups and their representations, Texts and Monographs in Physics, Springer, Berlin, 1997.
16 K. Mukoyama, Smooth SU(p, q)-actions on (2p+2q−1)-sphere and on the com-plex projective (p + q − 1)-space, Kyushu J. Math. 55 (2001), 213–236.   DOI   ScienceOn
17 T. Nagano, Transformation groups with (n - 1)-dimensional orbits on non-compact manifolds, Nagoya Math. J. 14 (1959), 25-38.   DOI