On the Non-existence of Certain Types of Weakly Symmetric Manifold
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...
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| Published in | Sarajevo journal of mathematics Vol. 2; no. 2; pp. 223 - 230 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
12.06.2024
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| Online Access | Get full text |
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| Summary: | 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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| ISSN: | 1840-0655 2233-1964 |
| DOI: | 10.5644/SJM.02.2.09 |