| Title:
|
Real hypersurfaces with constant totally real bisectional curvature in complex space forms (English) |
| Author:
|
Ortega, Miguel |
| Author:
|
Pérez, Juan de Dios |
| Author:
|
Suh, Young Jin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
377-388 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we classify real hypersurfaces with constant totally real bisectional curvature in a non flat complex space form $M_m(c)$, $c\ne 0$ as those which have constant holomorphic sectional curvature given in [6] and [13] or constant totally real sectional curvature given in [11]. (English) |
| Keyword:
|
real hypersurfaces |
| Keyword:
|
totally real bisectional curvature |
| Keyword:
|
sectional curvature |
| Keyword:
|
holomorphic sectional curvature |
| MSC:
|
53C12 |
| MSC:
|
53C15 |
| MSC:
|
53C40 |
| idZBL:
|
Zbl 1164.53367 |
| idMR:
|
MR2291743 |
| . |
| Date available:
|
2009-09-24T11:33:53Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128073 |
| . |
| Reference:
|
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| Reference:
|
[2] R. L. Bishop and S. I. Goldberg: Some implications of the generalized Gauss-Bonnet Theorem.Trans. Amer. Math. Soc. 112 (1964), 508–535. MR 0163271, 10.1090/S0002-9947-1964-0163271-8 |
| Reference:
|
[3] T. E. Cecil and P. J. Ryan: Focal sets and real hypersurfaces in complex projective space.Trans. A.M.S. 269 (1982), 481–499. MR 0637703 |
| Reference:
|
[4] S. I. Goldberg and S. Kobayashi: Holomorphic bisectional curvature.J. Diff. Geometry 1 (1967), 225–234. MR 0227901, 10.4310/jdg/1214428090 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Y. Maeda: On real hypersurfaces of a complex projective space.J. Math. Soc. Japan 28 (1976), 529–540. Zbl 0324.53039, MR 0407772, 10.2969/jmsj/02830529 |
| Reference:
|
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| Reference:
|
[9] R. Niebergall and P. J. Ryan: Real hypersurfaces in complex space forms.Tight and taut Submanifolds, edited by T. E. Cecil and S. S. Chern, Cambridge U. Press, 1997, pp. 233–305. MR 1486875 |
| Reference:
|
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| Reference:
|
[11] M. Ortega, J. D. Pérez and Y. J. Suh: Real hypersurfaces with constant totally real sectional curvature in a complex space form.Czechoslovak Math. J. 50 (2000), 531–537. MR 1777474, 10.1023/A:1022881510000 |
| Reference:
|
[12] J. D. Pérez and Y. J. Suh: Real hypersurfaces of quaternionic projective space satisfying ${\nabla }_{U_i}R=0$.Diff. Geom. and Its Appl. 7 (1997), 211–217. 10.1016/S0926-2245(97)00003-X |
| Reference:
|
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| Reference:
|
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| Reference:
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