Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane


Authors: Jürgen Berndt and José Carlos Díaz-Ramos
Journal: Proc. Amer. Math. Soc. 135 (2007), 3349-3357
MSC (2000): Primary 53C40; Secondary 53C55
DOI: https://doi.org/10.1090/S0002-9939-07-09012-0
Published electronically: June 19, 2007
MathSciNet review: 2322767
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We classify real hypersurfaces with constant principal curvatures in the complex hyperbolic plane. It follows from this classification that all of them are open parts of homogeneous ones.


References [Enhancements On Off] (What's this?)

  • 1. J. Berndt, Real hypersurfaces with constant principal curvatures in complex hyperbolic space, J. Reine Angew. Math. 395 (1989), 132-141. MR 983062 (90d:53062)
  • 2. J. Berndt, Homogeneous hypersurfaces in hyperbolic spaces, Math. Z. 229 (1998), 589-600. MR 1664778 (2001c:53065)
  • 3. J. Berndt, M. Brück, Cohomogeneity one actions on hyperbolic spaces, J. Reine Angew. Math. 541 (2001), 209-235. MR 1876290 (2002j:53059)
  • 4. J. Berndt, J.C. Díaz-Ramos, Real hypersurfaces with constant principal curvatures in complex hyperbolic space, J. London Math. Soc., (2) 74 (2006), 778-798. MR 983062 (90d:53062)
  • 5. J. Berndt, H. Tamaru, Cohomogeneity one actions on noncompact symmetric spaces of rank one, Trans. Amer. Math. Soc., 359 (2007), 3425-3438.
  • 6. É. Cartan, Familles de surfaces isoparamétriques dans les espaces à courbure constante, Ann. Mat. Pura Appl., IV. Ser. 17 (1938), 177-191. MR 1553310
  • 7. D. Cox, J. Little, D. O'Shea, Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra, Springer, New York, 1992. MR 1189133 (93j:13031)
  • 8. M. Lohnherr, On ruled real hypersurfaces of complex space forms, Ph.D. Thesis, University of Cologne, 1998.
  • 9. R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math. 10 (1973), 495-506. MR 0336660 (49:1433)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53C40, 53C55

Retrieve articles in all journals with MSC (2000): 53C40, 53C55


Additional Information

Jürgen Berndt
Affiliation: Department of Mathematics, University College, Cork, Ireland
Email: j.berndt@ucc.ie

José Carlos Díaz-Ramos
Affiliation: Department of Mathematics, University College, Cork, Ireland
Email: jc.diazramos@ucc.ie

DOI: https://doi.org/10.1090/S0002-9939-07-09012-0
Keywords: Homogeneous hypersurfaces, constant principal curvatures
Received by editor(s): May 16, 2006
Published electronically: June 19, 2007
Additional Notes: The second author has been supported by projects BFM 2003-02949 and PGIDIT 04 PXIC 20701 PN (Spain)
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society