Korean J. Math. Vol. 31 No. 2 (2023) pp.139-144
DOI: https://doi.org/10.11568/kjm.2023.31.2.139

Some theorems on recurrent manifolds and conformally recurrent manifolds

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Jaeman Kim


In this paper, we show that a recurrent manifold with harmonic curvature tensor is locally symmetric and that an Einstein and conformally recurrent manifold is locally symmetric. As a consequence, Einstein and recurrent manifolds must be locally symmetric. On the other hand, we have obtained some results for a (conformally) recurrent manifold with parallel vector field and also investigated some results for a (conformally) recurrent manifold with concircular vector field.

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