Homogeneous CR submanifolds of complex hyperbolic spaces

  1. Díaz-Ramos, José Carlos 1
  2. Domínguez-Vázquez, Miguel 1
  3. Pérez-Barral, Olga 2
  1. 1 Universidade de Santiago de Compostela
    info

    Universidade de Santiago de Compostela

    Santiago de Compostela, España

    ROR https://ror.org/030eybx10

  2. 2 IES Monte da Vila (O Grove, Galícia)
Journal:
Publicacions matematiques

ISSN: 0214-1493

Year of publication: 2023

Volume: 67

Issue: 0

Pages: 891-912

Type: Article

DOI: 10.5565/PUBLMAT6722315 DIALNET GOOGLE SCHOLAR lock_openDDD editor

More publications in: Publicacions matematiques

Abstract

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.

Bibliographic References

  • L. Bedulli and A. Gori, Homogeneous Lagrangian submanifolds, Comm. Anal. Geom. 16(3) (2008), 591–615. DOI: 10.4310/CAG.2008.v16.n3.a5
  • 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.
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