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P.J. Ryan's problem in semi-Riemannian space forms

Published online by Cambridge University Press:  19 July 2001

F. Defever ,
R. Deszcz ,
Z. Sentürk ,
L. Verstraelen  and
S. Yaprak
F. Defever
Affiliation:
Zuivere en Toegepaste Differentiaalmeetkunde, Departement Wiskunde K.U. Leuven, Celestijnenlaan 200 B, B-3001 Leuven, Belgium
R. Deszcz
Affiliation:
Department of Mathematics, Agricultural University of Wroclaw ul. Grunwaldzka 53 PL–50-357 Wroclaw, Poland
Z. Sentürk
Affiliation:
Department of Mathematics, Technical University of Istanbul 80626 Maslak, Istanbul, Turkey
L. Verstraelen
Affiliation:
Department Wiskunde, K.U. Leuven Celestijnenlaan 200 B, B-3001 Leuven, Belgium, Groep Exacte Wetenschappen, K.U. Brussel Vrijheidslaan 17, B-1080 Brussel, Belgium
S. Yaprak
Affiliation:
Department of Mathematics, University of Ankara 06100 Tandogan, Ankara, Turkey
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Abstract

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We prove that the conditions R·R=0 and R·S=0 are equivalent for hypersurfaces of a 5-dimensional semi-Riemannian space form N5(c). This solves a problem by P.J. Ryan in the case of hypersurfaces of dimension 4 in semi-Riemannian space forms.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 2 , May 1999 , pp. 271 - 281
Copyright
1999 Glasgow Mathematical Journal Trust