Characterizations of conformally flat hypersurfaces

Johan Deprez; Piet A. Verheyen; Leopold C. A. Verstraelen

Czechoslovak Mathematical Journal (1985)

  • Volume: 35, Issue: 1, page 140-145
  • ISSN: 0011-4642

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Deprez, Johan, Verheyen, Piet A., and Verstraelen, Leopold C. A.. "Characterizations of conformally flat hypersurfaces." Czechoslovak Mathematical Journal 35.1 (1985): 140-145. <http://eudml.org/doc/13498>.

@article{Deprez1985,
author = {Deprez, Johan, Verheyen, Piet A., Verstraelen, Leopold C. A.},
journal = {Czechoslovak Mathematical Journal},
keywords = {hypersurface; curvature tensor; conformally flat},
language = {eng},
number = {1},
pages = {140-145},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterizations of conformally flat hypersurfaces},
url = {http://eudml.org/doc/13498},
volume = {35},
year = {1985},
}

TY - JOUR
AU - Deprez, Johan
AU - Verheyen, Piet A.
AU - Verstraelen, Leopold C. A.
TI - Characterizations of conformally flat hypersurfaces
JO - Czechoslovak Mathematical Journal
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 1
SP - 140
EP - 145
LA - eng
KW - hypersurface; curvature tensor; conformally flat
UR - http://eudml.org/doc/13498
ER -

References

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  1. D. E. Blair P. Verheyen, L. Verstraelen, Hypersurfaces satisfaisant à R . C = 0 ou С . R = 0 , to appear. 
  2. E. Cartan, 10.24033/bsmf.975, Bull. Soc. Math. France, 45 (1917), p. 57-121. (1917) MR1504762DOI10.24033/bsmf.975
  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. (1977) Zbl0365.53007MR0478040
  4. J. Deprez P. Verheyen, L. Verstraelen, Intrinsic characterizations for complex hypercylinders and complex hyperspheres, Geom. Dedicata 16 (1984), 217-229. (1984) MR0758908
  5. G. L. Lancaster, 10.1215/S0012-7094-73-04001-5, Duke Math. J. 40 (1973), 1 - 8. (1973) Zbl0256.53024MR0320927DOI10.1215/S0012-7094-73-04001-5
  6. y. Matsuyarna, Complete hypersurfaces with R S = 0 in E n + 2 , Proc. Amer. Math. Soc. 88 (1983), 119-123. (1983) MR0691290
  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. (1972) Zbl0253.53018MR0326624
  8. K. Nomizu, 10.2748/tmj/1178243217, Tôhoku Math. J. 20(1968), 46-59. (1968) Zbl0174.53301MR0226549DOI10.2748/tmj/1178243217
  9. P. J. Ryan, 10.2748/tmj/1178242949, Tôhoku Math. J. 21 (1969), 363-388. (1969) MR0253243DOI10.2748/tmj/1178242949
  10. P. J. Ryan, Hypersurfaces with parallel Ricci tensor, Osaka J. Math. 8 (1971), 251 - 259. (1971) Zbl0222.53025MR0296859
  11. P. J. Ryan, 10.4064/cm-26-1-175-182, Colloq. Math. 26 (1972), 175-182. (1972) Zbl0243.53028MR0365437DOI10.4064/cm-26-1-175-182
  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. (1982) Zbl0508.53025MR0683165
  13. S. Tanno, Hypersurfaces satisfying a certain condition on the Ricci tensor, Tôhoku Math. J.21 (1969), 297-303. (1969) Zbl0189.22403MR0261508
  14. S. Tanno, T. Takahashi, 10.2748/tmj/1178242815, Tôhoku Math. J. 22 (1970), 212-219. (1970) Zbl0199.56502MR0268822DOI10.2748/tmj/1178242815
  15. T. Takahashi, 10.2969/jmsj/01920199, J. Math. Soc. Japan 19 (1967), 199-204. (1967) Zbl0147.40603MR0211371DOI10.2969/jmsj/01920199
  16. P. Verheyen, L. Verstraelen, A new intrinsic characterization of hyper cylinders in Euclidean spaces, to appear. 

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