Mathematica Bohemica

Mathematica Bohemica, first online, pp. 1-9

On quasirecurrent manifolds

Jaeman Kim

Received April 1, 2024. Published online December 6, 2024.

Abstract: We introduce a type of Riemannian manifolds (namely, quasirecurrent manifold) and study its several geometric properties. Among others, we prove that the scalar curvature of such a manifold is constant, and that the manifold is Einstein under certain condition. In addition, we deal with a quasirecurrent product manifold. Finally, we ensure the existence of quasirecurrent manifold by a proper example.

Keywords: quasirecurrent manifold; associated vector field; constant scalar curvature; Ricci symmetry; Einstein; cyclic Ricci symmetry; conformally flat; quasirecurrent product manifold; space of constant curvature

Classification MSC: 53A55, 53B20

DOI: 10.21136/MB.2024.0038-24

PDF available at: Institute of Mathematics CAS

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Affiliations: Jaeman Kim, Department of Mathematics Education, Kangwon National University, Chunchon 200-701, Kangwon Do, Republic of Korea, e-mail: jaeman64@kangwon.ac.kr

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