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On generalized recurrent Riemannian manifolds

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Abstract

The object of the present paper is to study a type of Riemannian manifolds called generalized recurrent manifolds. We have constructed two concrete examples of such a manifold whose scalar curvature is non-zero non-constant. Some other properties have been considered. Among others it is shown that on a generalized recurrent manifold with constant scalar curvature, Weyl-semisymmetry and semisymmetry are equivalent. Sufficient condition for a generalized recurrent manifold to be a special quasi Einstein manifold is obtained.

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Authors and Affiliations

  1. Department of Mathematics, Uludağ University, 16059, Bursa, Turkey

    K. Arslan & C. Murathan

  2. Department of Mathematics, Kalyani University, Kalyani, India

    U. C. De

  3. Department of Mathematics, Dumlupınar University, Kütahya, Turkey

    A. Yildiz

Authors
  1. K. Arslan
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  2. U. C. De
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  3. C. Murathan
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  4. A. Yildiz
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Corresponding author

Correspondence to K. Arslan.

Additional information

This work was done when second author visited Uludağ University during 12–31 October, 2006 supported by TUBITAK as an academic visitor.

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Arslan, K., De, U.C., Murathan, C. et al. On generalized recurrent Riemannian manifolds. Acta Math Hung 123, 27–39 (2009). https://doi.org/10.1007/s10474-008-8049-y

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