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