Projective domains with non-compact automorphism groups I
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Most of domains people have studied are convex bounded projective (or affine) domains. Edith Socie-Methou [15] characterized ellipsoid in Rn by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point
Abstract
Most of domains people have studied are convex bounded projective (or affine) domains. Edith Socie-Methou [15] characterized ellipsoid in Rn by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point
참고문헌 (18)
- E. Bedford, "Domains in C2 with noncompact groups of holomorphic automorphisms", mathematics of the USSR-Sbornik (N.S.), 135(2), pp.147~157 (1988), 141–151
- E. Bedford, "Domains in Cn+1 with noncompact automorphism group", Journal of Geometric Analysis, 1(3), pp.165~191 (1991)
- J. P. Benzecri, "Sur les varietes localement affines et localement projectives", Bulletin de la Société Mathématique de France, 88, pp.229~332 (1960)
- B. Colbois, "Rigidity of Hilbert metrics", Bulletin of the Australian Mathematical Society, 65(1), pp.23~34 (2002)
- W. M. Goldman, "Two examples of affine manifolds", Pacific Journal of Mathematics, 94(2), pp.327~330 (1981)
- W. M. Goldman, "Geometric structures on manifolds and varieties of representations, Geometry of group representations (Boulder, CO, 1987)", pp.169~198 (1988), Contemp. Math., 74, Amer. Math. Soc.
- W. M. Goldman, "Convex real projective structures on compact surfaces", Journal of Differential Geometry, 31(3), pp.791~845 (1990)
- H. Kim, "Actions of infinite discrete groups of projective transformation", Proc. Second GARC Symposium on Pure and Applied Math., pp.1~9
- K. T. Kim, "Complete localization of domains with noncompact automorphism groups", Transactions of the American Mathematical Society, 319(1), pp.139~153 (1990)
- K. T. Kim, "Geometry of bounded domains and the scaling techniques in several complex variables, Lecture Notes Series", pp.13~, Research Institutes of Mathematics Global Analysis Research Center, Seoul National University
- S. Kobayashi, "Projectively invariant distances for affine and projective structures, Differential geometry (Warsaw, 1979)", Banach Center Publications, 12, pp.127~152 (1984), PWN, Warsaw
- N. H. Kuiper, "On convex locally-projective spaces, Convegno Internazionale di Geometria Differenziale, Italia, 1953", pp.200~213 (1954), Edizioni Cremonese
- K. S. Park, "Some results on the geometry and topology of affine flat manifolds", 박사, pp.1997
- S. Pinchuk, "Holomorphic inequivalences of some classes of domains in Cn", Mathematics of the USSR-Sbornik, 39, pp.61~86 (1981)
- E. Socie-Methou, "Caracterisation des ellipsoides par leurs groupes d’automorphismes", Annales Scientifiques de Ecole Normale Superieure, 35(4), pp.538~548 (2002)
- J. Vey, "Sur les automorphismes affines des ouverts convexes saillants", Annali della Scuola Normale Superiore di Pisa Classe di Scienze, 24(3), pp.641~665 (1970)
- E. B. Vinberg, "Quasi-homogeneous cones", Mathematical Notes, 1(3), pp.231~235 (1967)
- C. W. Yi, "Projective domains with non-compact automorphism groups II, preprint", ~