On the Non-existence of Certain Types of Weakly Symmetric Manifold
DOI:
https://doi.org/10.5644/SJM.02.2.09Keywords:
Weakly symmetric manifold, quasi Einstein manifold, conformally flat Riemannian manifoldAbstract
An expression for the curvature tensor of a weakly symmetric manifold is obtained. Next it is shown that an Einstein weakly symmetric manifold of dimension $>2$ does not exist. Further it is proved that a conformally flat weakly symmetric manifold of dimension $>3$ is a quasi Einstein manifold. Finally a couple of results on conformally flat weakly symmetric manifold are presented.
2000 Mathematics Subject Classification. 53B35, 53B05
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References
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