Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SOME THEOREMS ON RECURRENT MANIFOLDS AND CONFORMALLY RECURRENT MANIFOLDS

  • Jaeman Kim (Department of Mathematics Education, Kangwon National University)
  • Received : 2023.02.07
  • Accepted : 2023.04.18
  • Published : 2023.06.30
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Abstract

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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Acknowledgement

The author would like to express his sincere thanks to the referee for valuable suggestions towards the improvement of this paper.

References

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