| Title:
|
Characterizations of conformally flat hypersurfaces (English) |
| Author:
|
Deprez, Johan |
| Author:
|
Verheyen, P. |
| Author:
|
Verstraelen, Leopold C. A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1985 |
| Pages:
|
140-145 |
| . |
| Category:
|
math |
| . |
| MSC:
|
53B25 |
| MSC:
|
53C40 |
| idZBL:
|
Zbl 0586.53001 |
| idMR:
|
MR779341 |
| DOI:
|
10.21136/CMJ.1985.102002 |
| . |
| Date available:
|
2008-06-09T15:03:54Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/102002 |
| . |
| Reference:
|
[1] D. E. Blair P. Verheyen, L. Verstraelen: Hypersurfaces satisfaisant à $R. C= 0$ ou $С . R=0$.to appear. |
| Reference:
|
[2] E. Cartan: La déformation des hypersurfaces dans l'espace conformément réel à $n \neq 5$ dimensions.Bull. Soc. Math. France, 45 (1917), p. 57-121. MR 1504762, 10.24033/bsmf.975 |
| Reference:
|
[3] В. Y. Chen, L. Verstraelen: A characterization of totally quasiumbilical submanifolds and its applications.Boll. Un. Mat. Ital. (5) 14-A (1977), 49-57. Zbl 0365.53007, MR 0478040 |
| Reference:
|
[4] J. Deprez P. Verheyen, L. Verstraelen: Intrinsic characterizations for complex hypercylinders and complex hyperspheres.Geom. Dedicata 16 (1984), 217-229. MR 0758908 |
| Reference:
|
[5] G. L. Lancaster: Canonical metrics for certain conformally Euclidean spaces of dimension three and codimension one.Duke Math. J. 40 (1973), 1 - 8. Zbl 0256.53024, MR 0320927, 10.1215/S0012-7094-73-04001-5 |
| Reference:
|
[6] y. Matsuyarna: Complete hypersurfaces with $RS = 0$ in $E\sp{n+2}$.Proc. Amer. Math. Soc. 88 (1983), 119-123. MR 0691290 |
| Reference:
|
[7] I. Mogi, H. Nakagawa: On hypersurfaces with parallel Ricci tensor in a Riemannian manifold of constant curvature.in Differential Geometry, in honor of K. Yano, Kinokuniya, 1972,267-279. Zbl 0253.53018, MR 0326624 |
| Reference:
|
[8] K. Nomizu: On hypersurfaces satisfying a certain condition on the curvature tensor.Tôhoku Math. J. 20(1968), 46-59. Zbl 0174.53301, MR 0226549, 10.2748/tmj/1178243217 |
| Reference:
|
[9] P. J. Ryan: Homogenity and some curvature conditions for hypersurfaces.Tôhoku Math. J. 21 (1969), 363-388. MR 0253243, 10.2748/tmj/1178242949 |
| Reference:
|
[10] P. J. Ryan: Hypersurfaces with parallel Ricci tensor.Osaka J. Math. 8 (1971), 251 - 259. Zbl 0222.53025, MR 0296859 |
| Reference:
|
[11] P. J. Ryan: A class of complex hypersurfaces.Colloq. Math. 26 (1972), 175-182. Zbl 0243.53028, MR 0365437, 10.4064/cm-26-1-175-182 |
| Reference:
|
[12] Z. I. Szabó: Structure theorems on Riemannian spaces satisfying $R(X, Y). R= 0$. I. The local version.J. Differential Geometry 17(1982) 531-582. Zbl 0508.53025, MR 0683165 |
| Reference:
|
[13] S. Tanno: Hypersurfaces satisfying a certain condition on the Ricci tensor.Tôhoku Math. J.21 (1969), 297-303. Zbl 0189.22403, MR 0261508 |
| Reference:
|
[14] S. Tanno, T. Takahashi: Some hypersurfaces of a sphere.Tôhoku Math. J. 22 (1970), 212-219. Zbl 0199.56502, MR 0268822, 10.2748/tmj/1178242815 |
| Reference:
|
[15] T. Takahashi: Hypersurface with parallel Ricci tensor in a space of constant holomorphic sectional curvature.J. Math. Soc. Japan 19 (1967), 199-204. Zbl 0147.40603, MR 0211371, 10.2969/jmsj/01920199 |
| Reference:
|
[16] P. Verheyen, L. Verstraelen: A new intrinsic characterization of hyper cylinders in Euclidean spaces.to appear. |
| . |
