Homogeneous Cauchy-Riemann structures

Krüger, Andreas

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 18 (1991) no. 2, pp. 193-212.

[1] A. Andreotti - G.A. Fredricks, Embeddability of real analytic Cauchy-Riemann manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), Vol. VI, 1 (1979), 285-304, MR 80h: 32019. | Numdam | MR | Zbl

[2] H. Azad, Levi-Curvature of manifolds with a Stein rational fibration, Manuscripta Math, 50 (1985), 269-311, MR 87i: 32046. | MR | Zbl

[3] H. Azad - A. Huckleberry - W. Richthofer, Homogeneous CR-manifolds, J. Reine Angew. Math. 358 (1985), 125-154, MR 87g: 32035. | MR | Zbl

[4] M.S. Baouendi - L.P. Rothschild, Embeddability of abstract CR structures and integrability of related systems, Ann. Inst. Fourier(Grenoble) 37.3 (1987), 131-141 (Their notion of "integrability" is different from the one adopted in this paper), MR 89c: 32053. | Numdam | MR | Zbl

[5] M.S. Baouendi - L.P. Rothschild - F. Treves, CR structures with group action and extendability of CR functions, Invent. Math. 82 (1985), 359-396, MR 87: 32028. | MR | Zbl

[6] A. Borel, Some remarks about Lie groups transitive on spheres and tori, Bull. Amer. Math. Soc. 55 (1949), 580-587, MR 10-680. | MR | Zbl

[7] A. Borel, Le plan projectif des octaves et les sphères comme espaces homogènes, C.R. Acad. Sci. Paris 230 (1950), 1378-1380, MR 11-640. | MR | Zbl

[8] D. Burns, JR. - S. Shnider, Spherical hypersurfaces in complex manifolds, Invent. Math. 33 (1976) 3, 223-246, MR 54# 7875. | MR | Zbl

[9] F. Ehlers - W.D. Neumann - J. Scherk, Links of surface singularities and CR space forms, Comment. Math. Helv. 62 (1987), 240-264, MR 88k: 32022. | MR | Zbl

[10] D. Feldmueller - R. Lehmann, Homogeneous CR-hypersurface-structures on spheres, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 14 (1987), 513-525. | Numdam | MR | Zbl

[11] A. Frölicher, Zur Differentialgeometrie der komplexen Strukturen, Math. Ann. 129 (1955), 50-95, MR 16-857. | MR | Zbl

[12] H. Gluck - F. Warner - W. Ziller, The geometry of the Hopf fibrations, Enseign. Math (2) 32 (1986), 173-198, MR 88e: 53067. | MR | Zbl

[13] S.J. Greenfield, Cauchy-Riemann equations in several variables, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 12 (1968), 275-314, MR 38# 6097. | Numdam | MR | Zbl

[14] R. Harvey - H.B. Lawsonjr., Calibrated geometries, Acta Math.148, (Uppsala 1982), 47-157, MR 85i: 53058. | MR | Zbl

[15] W.-C. Hsiang - W.-Y. Hsiang, Classification of differentiable actions on Sn, Rn, and Dn with Sk as the principal orbit type, Ann. of Math. (2) 82 (1965), 421-433, MR 31# 5922. | MR | Zbl

[16] A.T. Huckleberry - W. Richthofer, Recent developments in homogeneous CRhypersurfaces, in: A. Howard, P.-M. Wong (eds.): Contributions to several complex variables, (proceedings of a conference in honor of Wilhelm Stoll, held at Notre Dame, October, 1984) Vieweg Verlag, Braunschweig 1986, ISBN 3-528-08964-4, 149-177, MR 87k: 32057. | Zbl

[17] A.T. Huckleberry - D.M. Snow, Almost-homogeneous Kähler manifolds with hypersurface orbits, Osaka J. Math. 19 (1982), 763-786, MR 84i: 32042. | MR | Zbl

[18] A. Krüger, Homogeneous Cauchy-Riemann structures, Dissertation at the University of Notre Dame, IN, USA, April 1985; available through University Microfilms International, Ann Arbor, MI, USA.

[19] J.L. Koszul, Sur la forme hermitienne canonique des espaces homogènes complexes, Canad. J. Math. 7 (1955), 562-576, MR 17-1109. | MR | Zbl

[20] F.M. Malyšev, Complex homogeneous spaces of semisimple Lie groups of the first category, Math. USSR-Izv. 9 (1975), 939-950, MR 53# 5953. | MR | Zbl

[21] F.M. Malyšev, Complex homogeneous spaces of the Lie group SO(2k+1,2l+1), Math. USSR-Izv. 10 (1976), no. 4, 763-782, MR 54# 7876. | MR | Zbl

[22] F.M. Malyšev, Complex homogeneous spaces of semisimple Lie groups of type Dn, Math, USSR-Izv. 11 (1977), no. 4, MR 58# 17238. | Zbl

[23] D. Montgomery, Simply connected homogeneous spaces, Proc. Amer. Math. Soc. 1 (1950), 467-469, MR12-242. | MR | Zbl

[24] D. Montgomery - H. Samelson, Transformation groups on spheres, Ann. of Math. 44.3 (1943), 454-470, MR 5-60. | MR | Zbl

[25] A. Morimoto - T. Nagano, On pseudo-conformal transformations of hypersurfaces, J. Math. Soc. Japan 15.3 (1963), 289-300, MR 27# 5275. | MR | Zbl

[26] A.L. Oniščik, On Lie groups transitive on compact manifolds III, Math. USSR-Sb. 4.2 (1968), 233-240, MR 36# 6547, see also MR 40# 5795. | Zbl

[27] A.L. Oniščik, Decompositions of reductive Lie groups, Math. USSR-Sb. 9.4 (1969), 515-554, MR 43# 3393. | MR | Zbl

[28] J. Poncet, Groupes de Lie compacts de transformations de l'espace euclidien et les sphères comme espaces homogènes, Comment. Math. Helv. 33 (1959), 109-120, MR 21# 2708. | MR | Zbl

[29] H. Samelson, A class of complex-analytic manifolds, Portugal. Math. 12 (1953), 129-132, MR 15-505. | MR | Zbl

[30] T. Sasaki, Classification of left invariant complex structures on GL(2,R) and U(2), Kumamoto J. Math. 14 (1981), 115-123, MR 84b: 53050. | MR | Zbl

[31] T. Sasaki, Classification of left invariant complex structures on SL(3,R), Kumamoto J. Math. 15 (1982), 59-72, MR 84c: 32034. | MR | Zbl

[32] D.M. Snow, Invariant complex structures on reductive Lie groups, J. Reine Angew. Math. 371 (1986), 191-215, MR 87k: 32058. | MR | Zbl

[33] H.C. Wang, Closed manifolds with homogeneous complex structure, Amer. J. Math. 76 (1954), 1-32, MR 16-518. | MR | Zbl