Characterizations of conformally flat hypersurfaces
Czechoslovak Mathematical Journal, Tome 35 (1985) no. 1, pp. 140-145
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

DOI : 10.21136/CMJ.1985.102002
Classification : 53B25, 53C40
@article{10_21136_CMJ_1985_102002,
     author = {Deprez, Johan and Verheyen, P. and Verstraelen, Leopold C. A.},
     title = {Characterizations of conformally flat hypersurfaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {140--145},
     year = {1985},
     volume = {35},
     number = {1},
     doi = {10.21136/CMJ.1985.102002},
     mrnumber = {779341},
     zbl = {0586.53001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1985.102002/}
}
TY  - JOUR
AU  - Deprez, Johan
AU  - Verheyen, P.
AU  - Verstraelen, Leopold C. A.
TI  - Characterizations of conformally flat hypersurfaces
JO  - Czechoslovak Mathematical Journal
PY  - 1985
SP  - 140
EP  - 145
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1985.102002/
DO  - 10.21136/CMJ.1985.102002
LA  - en
ID  - 10_21136_CMJ_1985_102002
ER  - 
%0 Journal Article
%A Deprez, Johan
%A Verheyen, P.
%A Verstraelen, Leopold C. A.
%T Characterizations of conformally flat hypersurfaces
%J Czechoslovak Mathematical Journal
%D 1985
%P 140-145
%V 35
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1985.102002/
%R 10.21136/CMJ.1985.102002
%G en
%F 10_21136_CMJ_1985_102002
Deprez, Johan; Verheyen, P.; Verstraelen, Leopold C. A. Characterizations of conformally flat hypersurfaces. Czechoslovak Mathematical Journal, Tome 35 (1985) no. 1, pp. 140-145. doi: 10.21136/CMJ.1985.102002

[1] D. E. Blair P. Verheyen, L. Verstraelen: Hypersurfaces satisfaisant à $R. C= 0$ ou $С . R=0$. to appear.

[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. | DOI | MR

[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. | MR | Zbl

[4] J. Deprez P. Verheyen, L. Verstraelen: Intrinsic characterizations for complex hypercylinders and complex hyperspheres. Geom. Dedicata 16 (1984), 217-229. | MR

[5] G. L. Lancaster: Canonical metrics for certain conformally Euclidean spaces of dimension three and codimension one. Duke Math. J. 40 (1973), 1 - 8. | DOI | MR | Zbl

[6] y. Matsuyarna: Complete hypersurfaces with $RS = 0$ in $E\sp{n+2}$. Proc. Amer. Math. Soc. 88 (1983), 119-123. | MR

[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. | MR | Zbl

[8] K. Nomizu: On hypersurfaces satisfying a certain condition on the curvature tensor. Tôhoku Math. J. 20(1968), 46-59. | DOI | MR | Zbl

[9] P. J. Ryan: Homogenity and some curvature conditions for hypersurfaces. Tôhoku Math. J. 21 (1969), 363-388. | DOI | MR

[10] P. J. Ryan: Hypersurfaces with parallel Ricci tensor. Osaka J. Math. 8 (1971), 251 - 259. | MR | Zbl

[11] P. J. Ryan: A class of complex hypersurfaces. Colloq. Math. 26 (1972), 175-182. | DOI | MR | Zbl

[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. | MR | Zbl

[13] S. Tanno: Hypersurfaces satisfying a certain condition on the Ricci tensor. Tôhoku Math. J.21 (1969), 297-303. | MR | Zbl

[14] S. Tanno, T. Takahashi: Some hypersurfaces of a sphere. Tôhoku Math. J. 22 (1970), 212-219. | DOI | MR | Zbl

[15] T. Takahashi: Hypersurface with parallel Ricci tensor in a space of constant holomorphic sectional curvature. J. Math. Soc. Japan 19 (1967), 199-204. | DOI | MR | Zbl

[16] P. Verheyen, L. Verstraelen: A new intrinsic characterization of hyper cylinders in Euclidean spaces. to appear.

Cité par Sources :