Almost contact Riemannian three-manifolds with Reeb flow symmetry. (English) Zbl 1472.53091
J. T. Cho and M. Kimura [Differ. Geom. Appl. 35, 266–273 (2014; Zbl 1319.53094)] studied almost Kenmotsu three-manifolds whose Ricci operator is invariant along the Reeb flow. They claim to obtain a classification result for such manifolds, but unfortunately the proof presents some problems (cf. Remark 4.1). The aim of the paper under review is to correct the classification. Therefore, using the canonical foliation on such spaces, the author obtains the complete classification of simply connected homogeneous almost \(\alpha\)-Kenmotsu three-manifolds whose Ricci operator is invariant along the Reeb flow (cf. Theorem 1.2).
Reviewer: Gabriel Eduard Vilcu (Ploieşti)
MSC:
| 53D15 | Almost contact and almost symplectic manifolds |
| 53C30 | Differential geometry of homogeneous manifolds |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53C12 | Foliations (differential geometric aspects) |
Keywords:
almost \(\alpha\)-Kenmotsu three-manifolds; Reeb flow; Ricci operator; non-unimodular Lie groups; Gaussian and extrinsic curvatureCitations:
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