A Ricci-semi-symmetric hypersurface of Euclidean space which is not semi-symmetric

Authors:
Bahaa E. Abdalla and Franki Dillen

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1805-1808

MSC (1991):
Primary 53B25

DOI:
https://doi.org/10.1090/S0002-9939-01-06220-7

Published electronically:
December 20, 2001

MathSciNet review:
1887029

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Abstract | References | Similar Articles | Additional Information

Abstract: We construct the first explicit example of a Ricci-semi-symmetric hypersurface of Euclidean space which is not semi-symmetric.

**1.**F. Defever,*Solution of a problem of P.J. Ryan*, preprint 1999.**2.**F. Defever, R. Deszcz, Z. Senturk, L. Verstraelen, S. Yaprak,*P.J. Ryan's problem in semi-Euclidean spaces*, Glasgow Math. J.,**41**(1999), pp. 271-281. MR**2000d:53054****3.**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.**4.**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.**5.**Y. Matsuyama,*Complete hypersurfaces with in*, Proc. Amer. Math. Soc.**88**(1983), pp. 119-123. MR**84h:53023****6.**K. Nomizu,*On hypersurfaces satisfying a certain condition on the curvature tensor*, Tôhoku Math. J.**20**(1968), pp. 46-59. MR**37:2138****7.**P. J. Ryan,*Hypersurfaces with parallel Ricci tensor*, Osaka J. Math.**8**(1971), pp. 251-259. MR**45:5918****8.**-,*A class of complex hypersurfaces*, Colloq. Math.**26**(1972), pp. 175-182. MR**51:1689**

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Additional 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

DOI:
https://doi.org/10.1090/S0002-9939-01-06220-7

Keywords:
Semi-symmetric,
Ricci-semi-symmetric,
hypersurface

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

Article copyright:
© Copyright 2001
American Mathematical Society