|
Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane
Author(s):
Jürgen
Berndt;
José
Carlos
Díaz-Ramos
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3349-3357.
MSC (2000):
Primary 53C40;
Secondary 53C55
Posted:
June 19, 2007
Retrieve article in:
PDF DVI PostScript
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:
-
- 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:
10.1090/S0002-9939-07-09012-0
PII:
S 0002-9939(07)09012-0
Keywords:
Homogeneous hypersurfaces,
constant principal curvatures
Received by editor(s):
May 16, 2006
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org