×

zbMATH — the first resource for mathematics

A classification of Riemannian 3-manifolds with constant principal Ricci curvatures. (English) Zbl 0788.53038
The aim of this paper is to give the classification mentioned in the title locally and in a “quasi-explicit” form. In particular, it is proved that the local isometry classes of Riemannian 3-manifolds with the prescribed constant principal Ricci curvatures as in the title depend on two arbitrary functions of one variable. Moreover, explicit examples are given with such constant Ricci eigenvalues which are never reached by a homogeneous Riemannian 3-manifold.
Reviewer: O.Kowalski (Praha)

MSC:
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C30 Differential geometry of homogeneous manifolds
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.2969/jmsj/04430461 · Zbl 0762.53031 · doi:10.2969/jmsj/04430461
[2] DOI: 10.1016/S0001-8708(76)80002-3 · Zbl 0341.53030 · doi:10.1016/S0001-8708(76)80002-3
[3] C. R. Acad. Sci. Paris 311 pp 355– (1990)
[4] I (1963)
[5] Comment. Math. Univ. Carolinae 30 pp 85– (1989)
[6] Nagoya Math. J. 123 pp 77– (1991) · Zbl 0738.53032 · doi:10.1017/S0027763000003652
[7] preprint (1992)
[8] Proceedings of the Curvature Geometry Workshop pp 35– (1989)
[9] DOI: 10.1007/BF01219082 · Zbl 0443.53037 · doi:10.1007/BF01219082
[10] Ann. Sci. École Norm. Sup. 22 pp 535– (1989) · Zbl 0698.53033 · doi:10.24033/asens.1592
[11] DOI: 10.1007/BF01389010 · Zbl 0489.53014 · doi:10.1007/BF01389010
[12] 40 pp 221– (1988)
[13] (1987)
[14] DOI: 10.2748/tmj/1178241081 · Zbl 0302.53022 · doi:10.2748/tmj/1178241081
[15] Tensor, N.S. 31 pp 87– (1977)
[16] 26 pp 343– (1975)
[17] J. Math. Pures Appl. 71 pp 471– (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.