Almost Contact Metric Manifolds with Local Riemannian and Ricci Symmetries

  • Yaning WangEmail author


In this paper, we show that the Reeb sectional curvature of a locally symmetric almost coKähler manifold \(M^{2n+1}\) is a constant if and only if \(M^{2n+1}\) is locally isometric to the product of \(\mathbb {R}\) and a locally symmetric almost Kähler manifold. Similar result in the framework of almost Kenmotsu manifolds is established. We give a characterization for a Ricci symmetric almost Kenmotsu manifold to be Einstein.


Almost coKähler manifold almost Kenmotsu manifold local symmetry Ricci symmetry 

Mathematics Subject Classification

Primary 53D15 Secondary 53C25 



This work was supported by the Youth Science Foundation of Henan Normal University (No. 2014QK01). The author would like to thank the reviewer for his or her useful suggestions.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information SciencesHenan Normal UniversityXinxiangPeople’s Republic of China

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