A Ricci-semi-symmetric hypersurface of Euclidean space which is not semi-symmetric
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- by Bahaa E. Abdalla and Franki Dillen
- Proc. Amer. Math. Soc. 130 (2002), 1805-1808
- DOI: https://doi.org/10.1090/S0002-9939-01-06220-7
- Published electronically: December 20, 2001
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Abstract:
We construct the first explicit example of a Ricci-semi-symmetric hypersurface of Euclidean space which is not semi-symmetric.References
- F. Defever, Solution of a problem of P.J. Ryan, preprint 1999.
- F. Defever, R. Deszcz, Z. Sentürk, L. Verstraelen, and S. Yaprak, P. J. Ryan’s problem in semi-Riemannian space forms, Glasg. Math. J. 41 (1999), no. 2, 271–281. MR 1700030, DOI 10.1017/S0017089599970969
- R. Deszcz, On the equivalence of Ricci-semisymmetry and semisymmetry, Department of Mathematics, Agricultural University Wroclaw, Ser. A, Theory and Methods, Preprint No. 64, Wroclaw 1998.
- R. Deszcz and M. Glogowska, Examples of nonsemisymmetric Ricci-semisymmetric hypersurfaces, Department of Mathematics, Agricultural University Wroclaw, Ser. A, Theory and Methods, Preprint No. 79, Wroclaw 2000.
- Yoshio Matsuyama, Complete hypersurfaces with $RS=0$ in $E^{n+1}$, Proc. Amer. Math. Soc. 88 (1983), no. 1, 119–123. MR 691290, DOI 10.1090/S0002-9939-1983-0691290-9
- Katsumi Nomizu, On hypersurfaces satisfying a certain condition on the curvature tensor, Tohoku Math. J. (2) 20 (1968), 46–59. MR 226549, DOI 10.2748/tmj/1178243217
- Patrick J. Ryan, Hypersurfaces with parallel Ricci tensor, Osaka Math. J. 8 (1971), 251–259. MR 296859
- Patrick J. Ryan, A class of complex hypersurfaces, Colloq. Math. 26 (1972), 175–182, 385. MR 365437, DOI 10.4064/cm-26-1-175-182
Bibliographic Information
- Bahaa E. Abdalla
- Affiliation: Department of Mathematics, College of Science, King Fahd University of Petroleum and Minerals, Box 859, Dhahran 31261, Saudi Arabia
- Address at time of publication: Prince Sultan Private College, Riyadh 11586, P.O. Box 66833, Kingdom of Saudi Arabia
- Email: b_abdalla@hotmail.com
- Franki Dillen
- Affiliation: Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium
- Email: Franki.Dillen@wis.kuleuven.ac.be
- Received by editor(s): July 28, 2000
- Received by editor(s) in revised form: November 28, 2000
- Published electronically: December 20, 2001
- Additional Notes: The second author is a Postdoctoral Research Fellow of the Fund for Scientific Research–Flanders.
- Communicated by: Wolfgang Ziller
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1805-1808
- MSC (1991): Primary 53B25
- DOI: https://doi.org/10.1090/S0002-9939-01-06220-7
- MathSciNet review: 1887029