Geodesic
Hyperbolic Manifolds with High-Dimensional Automorphism Group
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 245-266.

Voir la notice de l'article provenant de la source Math-Net.Ru

We survey our recent classification results for Kobayashi-hyperbolic $n$-dimensional manifolds with holomorphic automorphism group of dimension at least $n^2-1$ for $n\ge 2$. 
@article{TM_2006_253_a18,
     author = {A. V. Isaev},
     title = {Hyperbolic {Manifolds} with {High-Dimensional} {Automorphism} {Group}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {245--266},
     publisher = {mathdoc},
     volume = {253},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_253_a18/}
}
TY  - JOUR
AU  - A. V. Isaev
TI  - Hyperbolic Manifolds with High-Dimensional Automorphism Group
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2006
SP  - 245
EP  - 266
VL  - 253
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2006_253_a18/
LA  - en
ID  - TM_2006_253_a18
ER  - 
%0 Journal Article
%A A. V. Isaev
%T Hyperbolic Manifolds with High-Dimensional Automorphism Group
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2006
%P 245-266
%V 253
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2006_253_a18/
%G en
%F TM_2006_253_a18
A. V. Isaev. Hyperbolic Manifolds with High-Dimensional Automorphism Group. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 245-266. http://geodesic.mathdoc.fr/item/TM_2006_253_a18/

[1] Alekseevsky A.V., Alekseevsky D.V., “Riemann $G$-manifolds with one-dimensional orbit space”, Ann. Global Anal. and Geom., 11 (1993), 197–211 | MR | Zbl

[2] Bochner S., Montgomery D., “Locally compact groups of differentiable transformations”, Ann. Math. Ser. 2, 47 (1946), 639–653 | DOI | MR | Zbl

[3] Burns D., Shnider S., “Spherical hypersurfaces in complex manifolds”, Invent. math., 33 (1976), 223–246 | DOI | MR | Zbl

[4] Cartan E., “Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes. I, II”, Ann. Mat. Pura ed Appl., 11 (1932), 17–90 ; Ann. Scuola Norm. Super. Pisa, 1 (1932), 333–354 ; Oeuvres completes, Pt. 2, V. 2, Gauthier-Villars, Paris, 1953, 1231–1304; Pt. 3, V. 2, 1955 | DOI | MR | Zbl | MR | Zbl

[5] van Dantzig D., van der Waerden B.L., “Über metrisch homogene Räume”, Abh. Math. Sem. Hamburg, 6 (1928), 367–376 | DOI | Zbl

[6] Ezhov V.V., Isaev A.V., “On the dimension of the stability group for a Levi non-degenerate hypersurface”, Ill. J. Math., 49 (2005), 1155–1169 | MR | Zbl

[7] Gifford J.A., Isaev A.V., Krantz S.G., “On the dimensions of the automorphism groups of hyperbolic Reinhardt domains”, Ill. J. Math., 44 (2000), 602–618 | MR | Zbl

[8] Greene R.E., Krantz S.G., “Characterization of complex manifolds by the isotropy subgroups of their automorphism groups”, Indiana Univ. Math. J., 34 (1985), 865–879 | DOI | MR | Zbl

[9] Isaev A.V., “On hyperbolic $n$-dimensional manifolds with automorphism group of dimension $n^2$”, Complex Variables, 50 (2005), 345–355 | MR | Zbl

[10] Isaev A.V., “Hyperbolic $n$-dimensional manifolds with automorphism group of dimension $n^2$”, Geom. and Funct. Anal. (to appear) | MR

[11] Isaev A.V., “Hyperbolic manifolds of dimension $n$ with automorphism group of dimension $n^2-1$”, J. Geom. Anal., 15 (2005), 239–259 | MR | Zbl

[12] Isaev A., “Analogues of Rossi's map and E. Cartan's classification of homogeneous strongly pseudoconvex 3-dimensional hypersurfaces”, J. Lie Theory, 16 (2006), 407–426 | MR | Zbl

[13] Isaev A.V., Hyperbolic 2-dimensional manifolds with 3-dimensional automorphism groups, math.CV/0507199 | MR

[14] Isaev A.V., Hyperbolic 2-dimensional manifolds with 3-dimensional automorphism group, math.CV/0509030 | MR

[15] Isaev A.V., Krantz S.G., “On the automorphism groups of hyperbolic manifolds”, J. reine und angew. Math., 534 (2001), 187–194 | MR | Zbl

[16] Kaup W., “Reelle Transformationsgruppen und invariante Metriken auf komplexen Räumen”, Invent. math., 3 (1967), 43–70 | DOI | MR | Zbl

[17] Kaup W., Matsushima Y., Ochiai T., “On the automorphisms and equivalences of generalized Siegel domains”, Amer. J. Math., 92 (1970), 475–497 | DOI | MR

[18] Kim K.-T., Verdiani L., “Complex $n$-dimensional manifolds with a real $n^2$-dimensional automorphism group”, J. Geom. Anal., 14 (2004), 701–713 | MR | Zbl

[19] Kobayashi S., Hyperbolic manifolds and holomorphic mappings, M. Dekker, New York, 1970 | MR | Zbl

[20] Kobayashi S., Transformation groups in differential geometry, Springer, Berlin; Heidelberg; New York, 1972 | MR

[21] Kruzhilin N.G., “Golomorfnye avtomorfizmy giperbolicheskikh oblastei Reinkhardta”, Izv. AN SSSR. Ser. mat., 52:1 (1988), 16–40 | MR | Zbl

[22] Nakajima K., “Homogeneous hyperbolic manifolds and homogeneous Siegel domains”, J. Math. Kyoto Univ., 25 (1985), 269–291 | MR | Zbl

[23] Pyatetskii-Shapiro I.I., Geometriya klassicheskikh oblastei i teoriya avtomorfnykh funktsii, Fizmatgiz, M., 1961 | MR

[24] Rossi H., “Attaching analytic spaces to an analytic space along a pseudoconcave boundary”, Proc. Conf. Complex Analysis (Minneapolis, 1964), Springer, Berlin, 1965, 242–256 | MR

[25] Satake I., Algebraic structures of symmetric domains, Kanô Mem. Lect. 4. Publ. Math. Soc. Japan, 14, Princeton Univ. Press, Princeton, 1980 | MR | Zbl