期刊
RESULTS IN MATHEMATICS
卷 75, 期 4, 页码 -出版社
SPRINGER BASEL AG
DOI: 10.1007/s00025-020-01267-4
关键词
Ricci-like soliton; eta-Ricci soliton; Einstein-like manifold; eta-Einstein manifold; almost contact B-metric manifold; almost contact complex Riemannian manifold
资金
- Medical University of Plovdiv
- University of Plovdiv Paisii Hilendarski, Bulgaria [MU19-FMI-020, FP19-FMI-002]
Ricci-like solitons on Sasaki-like almost contact B-metric manifolds are the object of study. Cases, where the potential of the Ricci-like soliton is the Reeb vector field or pointwise collinear to it, are considered. In the former case, the properties for a parallel or recurrent Ricci-tensor are studied. In the latter case, it is shown that the potential of the considered Ricci-like soliton has a constant length and the manifold is eta-Einstein. Other curvature conditions are also found, which imply that the main metric is Einstein. After that, some results are obtained for a parallel symmetric second-order covariant tensor on the manifolds under study. Finally, an explicit example of dimension 5 is given and some of the results are illustrated.
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