Finally, it is obtained that a quasi-conformally flat normal metric contact pair manifold is an Einstein manifold with a positive scalar curvature and, is a space of constant curvature.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, the geometry of normal metric contact pair manifolds is studied under the flatness of conformal, concircular and quasi-conformal curvature tensors.
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Key Findings & Data:It is proved that a conformal flat normal metric contact pair manifold is an Einstein manifold with a positive scalar curvature and has positive sectional curvature.
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Conclusion & Impact:Finally, it is obtained that a quasi-conformally flat normal metric contact pair manifold is an Einstein manifold with a positive scalar curvature and, is a space of constant curvature.
In this paper, the geometry of normal metric contact pair manifolds is studied under the flatness of conformal, concircular and quasi-conformal curvature tensors. It is proved that a conformal flat normal metric contact pair manifold is an Einstein manifold with a positive scalar curvature and has positive sectional curvature. It is also shown that a concircular flat normal metric contact pair manifold is an Einstein manifold. Finally, it is obtained that a quasi-conformally flat normal metric contact pair manifold is an Einstein manifold with a positive scalar curvature and, is a space of constant curvature.
Ünal, İ. (2020). Some flatness conditions on normal metric contact pairs. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 2. https://doi.org/10.31801/cfsuasmas.546701
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