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A classification of Riemannian 3-manifolds with constant principal ricci curvaturesρ1= ρ2≠ ρ3

Published online by Cambridge University Press:  22 January 2016

Oldřich Kowalski
Oldřich Kowalski*
Affiliation:
Faculty of Mathematics and Physics Charles UniversitySokolovská 83, 186 00 PrahaCzech Republic
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This paper has been motivated by various problems and results in differential geometry. The main motivation is the study of curvature homogeneous Riemannian spaces initiated in 1960 by I.M. Singer (see Section 9—Appendix for the precise definitions and references). Up to recently, only sporadic classes of examples have been known of curvature homogeneous spaces which are not locally homogeneous. For instance, isoparametric hypersurfaces in space forms give nice examples of nontrivial curvature homogeneous spaces (see [FKM]). To study the topography of curvature homogeneous spaces more systematically, it is natural to start with the dimension n = 3. The following results and problems have been particularly inspiring.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 132 , December 1993 , pp. 1 - 36
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

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