Korean J. Math. Vol. 30 No. 1 (2022) pp.61-66
DOI: https://doi.org/10.11568/kjm.2022.30.1.61

A type of weakly symmetric structure on a Riemannian manifold

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Published: Mar 30, 2022
Keywords:
semirecurrent manifold, conformally recurrent, concircularly recurrent, Riemannian product manifold
Mathematics Subject Classification:
53A55, 53B20

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Jaeman Kim
Department of Mathematics Education, Kangwon National University, Chunchon 24341, Korea

Abstract

A new type of Riemannian manifold called semirecurrent manifold has been defined and some of its geometric properties are studied. Among others we show that the scalar curvature of semirecurrent manifold is constant and hence semirecurrent manifold is also concircularly recurrent. In addition, we show that the associated 1-form (resp. the associated vector field) of semirecurrent manifold is closed (resp. an eigenvector of its Ricci tensor). Furthermore, we prove that if a Riemannian product manifold is semirecurrent, then either one decomposition manifold is locally symmetric or the other decomposition manifold is a space of constant curvature.


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