On generalized recurrent Riemannian manifolds |
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Authors: | K Arslan U C De C Murathan A Yildiz |
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Institution: | 1. Department of Mathematics, Uluda? University, 16059, Bursa, Turkey 2. Department of Mathematics, Kalyani University, Kalyani, India 3. Department of Mathematics, Dumlup?nar University, Kütahya, Turkey
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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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