| Title:
|
Ricci curvature of real hypersurfaces in complex hyperbolic space (English) |
| Author:
|
Chen, Bang-Yen |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
73-80 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality. (English) |
| Keyword:
|
Ricci curvature |
| Keyword:
|
shape operator |
| Keyword:
|
real hypersurface |
| Keyword:
|
algebraic lemma |
| Keyword:
|
tubular hypersurface |
| Keyword:
|
horosphere |
| Keyword:
|
complex hyperbolic space |
| MSC:
|
53B25 |
| MSC:
|
53C40 |
| MSC:
|
53C42 |
| idZBL:
|
Zbl 1087.53052 |
| idMR:
|
MR1899570 |
| . |
| Date available:
|
2008-06-06T22:29:56Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107821 |
| . |
| Reference:
|
[1] Berndt, J.: Real hypersurfaces with constant principal curvatures in complex hyperbolic space.J. Reine Angew. Math. 395 (1989), 132-141. Zbl 0655.53046, MR 0983062 |
| Reference:
|
[2] Chen, B. Y.: Geometry of Submanifolds.M. Dekker, New York, 1973. MR 0353212 |
| Reference:
|
[3] Chen, B. Y.: Some pinching and classification theorems for minimal submanifolds.Arch. Math. (Basel) 60 (1993), 568–578. Zbl 0811.53060, MR 1216703 |
| Reference:
|
[4] Chen, B. Y.: A general inequality for submanifolds in complex-space-forms and its applications.Arch. Math. (Basel) 67 (1996), 519–528. Zbl 0871.53043, MR 1418914 |
| Reference:
|
[5] Chen, B. Y.: Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimension.Glasgow Math. J. 41 (1999), 33-41. MR 1689730 |
| Reference:
|
[6] De Smet, P. J., Dillen, F., Verstraelen, L. and Vrancken, L.: The normal curvature of totally real submanifolds of $S^6(1)$.Glasgow Math. J. 40 (1998), 199–204. MR 1630238 |
| Reference:
|
[7] De Smet, P. J., Dillen, F., Verstraelen, L. and Vrancken, L.: A pointwise inequality in submanifold theory.Arch. Math. (Brno) 35 (1999), 115–128. MR 1711669 |
| . |
