Homogeneous CR submanifolds of complex hyperbolic spaces
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Jose Carlos Díaz-Ramos
Universidade de Santiago de Compostela
Miguel Domínguez-Vázquez
Universidade de Santiago de Compostela
Olga Pérez-Barral
IES Monte da Vila (O Grove, Galícia)
We classify homogeneous CR submanifolds in complex hyperbolic spaces arising as orbits of a subgroup of the solvable part of the Iwasawa decomposition of the isometry group of the ambient space.
Paraules clau
complex hyperbolic space, CR submanifold, homogeneous submanifold
Article Details
Com citar
Díaz-Ramos, Jose Carlos et al. “Homogeneous CR submanifolds of complex hyperbolic spaces”. Publicacions Matemàtiques, vol.VOL 67, no. 2, pp. 891-12, https://raco.cat/index.php/PublicacionsMatematiques/article/view/418526.
Referències
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J. Berndt and M. Brück, Cohomogeneity one actions on hyperbolic spaces, J. Reine Angew. Math. 541 (2001), 209–235. DOI: 10.1515/crll.2001.093
J. Berndt and J. C. Díaz-Ramos, Homogeneous hypersurfaces in complex hyperbolic spaces, Geom. Dedicata 138 (2009), 129–150. DOI: 10.1007/s10711-008-9303-8
J. Berndt and H. Tamaru, Cohomogeneity one actions on noncompact symmetric spaces of rank one, Trans. Amer. Math. Soc. 359(7) (2007), 3425–3438. DOI: 10.1090/S0002-9947-07-04305-X
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J. C. Díaz-Ramos, M. Domínguez Vazquez, and A. Kollross, Polar actions on complex hyperbolic spaces, Math. Z. 287(3-4) (2017), 1183–1213.
DOI: 10.1007/s00209-017-1864-5
J. C. Díaz-Ramos, M. Domínguez-Vazquez, and V. Sanmartín-López, Isoparametric hypersurfaces in complex hyperbolic spaces, Adv. Math. 314
(2017), 756–805. DOI: 10.1016/j.aim.2017.05.012
J. C. Díaz-Ramos, S. M. B. Kashani, and M. J. Vanaei, Cohomogeneity one actions on anti de Sitter spacetimes, Results Math. 72(1-2) (2017), 515–536.
DOI: 10.1007/s00025-017-0672-x
M. Djoric and M. Okumura, “CR Submanifolds of Complex Projective Space”, Developments in Mathematics 19, Springer, New York, 2010. DOI: 10.1007/978-1-4419-0434-8
P. B. Eberlein, “Geometry of Nonpositively Curved Manifolds”, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1996.
T. Hashinaga and T. Kajigaya, A class of non-compact homogeneous Lagrangian submanifolds in complex hyperbolic spaces, Ann. Global Anal. Geom.
51(1) (2017), 21–33. DOI: 10.1007/s10455-016-9521-5
Y. Ohnita, Certain Lagrangian submanifolds in Hermitian symmetric spaces and Hamiltonian stability problems, in: “Proceedings of the 15th International Workshop on Differential Geometry and the 4th KNUGRG-OCAMI Differential Geometry Workshop”, Vol. 15, Natl. Inst. Math. Sci. (NIMS), Taej˘on, 2011, pp. 209–234.
F. Podesta and G. Thorbergsson, Polar and coisotropic actions on Kähler manifolds, Trans. Amer. Math. Soc. 354(5) (2002), 1759–1781.
DOI: 10.1090/S0002-9947-02-02902-1
R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka Math. J. 10 (1973), 495–506.
M. Takeuchi, Homogeneous Kähler submanifolds in complex projective spaces, Japan. J. Math. (N.S.) 4(1) (1978), 171–219.
A. Bejancu, “Geometry of CR-Submanifolds”, Mathematics and its Applications (East European Series) 23, D. Reidel Publishing Co., Dordrecht, 1986.
DOI: 10.1007/978-94-009-4604-0
J. Berndt and M. Brück, Cohomogeneity one actions on hyperbolic spaces, J. Reine Angew. Math. 541 (2001), 209–235. DOI: 10.1515/crll.2001.093
J. Berndt and J. C. Díaz-Ramos, Homogeneous hypersurfaces in complex hyperbolic spaces, Geom. Dedicata 138 (2009), 129–150. DOI: 10.1007/s10711-008-9303-8
J. Berndt and H. Tamaru, Cohomogeneity one actions on noncompact symmetric spaces of rank one, Trans. Amer. Math. Soc. 359(7) (2007), 3425–3438. DOI: 10.1090/S0002-9947-07-04305-X
J. Berndt, F. Tricerri, and L. Vanhecke, “Generalized Heisenberg Groups and Damek–Ricci Harmonic Spaces”, Lecture Notes in Mathematics 1598,
Springer-Verlag, Berlin, 1995. DOI: 10.1007/BFb0076902
A. J. Di Scala, H. Ishi, and A. Loi, Kähler immersions of homogeneous Kähler manifolds into complex space forms, Asian J. Math. 16(3) (2012), 479–487.
DOI: 10.4310/AJM.2012.v16.n3.a7
J. C. Díaz-Ramos, M. Domínguez Vazquez, and A. Kollross, Polar actions on complex hyperbolic spaces, Math. Z. 287(3-4) (2017), 1183–1213.
DOI: 10.1007/s00209-017-1864-5
J. C. Díaz-Ramos, M. Domínguez-Vazquez, and V. Sanmartín-López, Isoparametric hypersurfaces in complex hyperbolic spaces, Adv. Math. 314
(2017), 756–805. DOI: 10.1016/j.aim.2017.05.012
J. C. Díaz-Ramos, S. M. B. Kashani, and M. J. Vanaei, Cohomogeneity one actions on anti de Sitter spacetimes, Results Math. 72(1-2) (2017), 515–536.
DOI: 10.1007/s00025-017-0672-x
M. Djoric and M. Okumura, “CR Submanifolds of Complex Projective Space”, Developments in Mathematics 19, Springer, New York, 2010. DOI: 10.1007/978-1-4419-0434-8
P. B. Eberlein, “Geometry of Nonpositively Curved Manifolds”, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1996.
T. Hashinaga and T. Kajigaya, A class of non-compact homogeneous Lagrangian submanifolds in complex hyperbolic spaces, Ann. Global Anal. Geom.
51(1) (2017), 21–33. DOI: 10.1007/s10455-016-9521-5
Y. Ohnita, Certain Lagrangian submanifolds in Hermitian symmetric spaces and Hamiltonian stability problems, in: “Proceedings of the 15th International Workshop on Differential Geometry and the 4th KNUGRG-OCAMI Differential Geometry Workshop”, Vol. 15, Natl. Inst. Math. Sci. (NIMS), Taej˘on, 2011, pp. 209–234.
F. Podesta and G. Thorbergsson, Polar and coisotropic actions on Kähler manifolds, Trans. Amer. Math. Soc. 354(5) (2002), 1759–1781.
DOI: 10.1090/S0002-9947-02-02902-1
R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka Math. J. 10 (1973), 495–506.
M. Takeuchi, Homogeneous Kähler submanifolds in complex projective spaces, Japan. J. Math. (N.S.) 4(1) (1978), 171–219.