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Journals / Turkish Journal of Mathematics and Computer Science / 2020 / Volume: 12 Issue: 2

On Quasi-Conformal Flat Para-Sasakian Manifolds

İnan Ünal(MUNZUR UNIVERSITY)0000-0003-1318-9685
Ramazan Sarı(AMASYA UNIVERSITY)0000-0002-4618-8243
Pages
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Publication Date
2020-12-31
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Finally, we work on the sectional curvature properties of an invariant submanifold of a quasi-conformally flat para-Sasakian manifold.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we present some new results on invariant submanifolds of a para-Sasakian manifold under the quasi-conformally flatness condition.
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Key Findings & Data:Firstly, we examine flatness of quasi-conformal curvature tensor on para-Sasakian manifolds.
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Conclusion & Impact:Finally, we work on the sectional curvature properties of an invariant submanifold of a quasi-conformally flat para-Sasakian manifold.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Para-Sasakian manifold · invariant submanifolds · quasi-conformal curvature tensor

Abstract

In this paper, we present some new results on invariant submanifolds of a para-Sasakian manifold under the quasi-conformally flatness condition. Firstly, we examine flatness of quasi-conformal curvature tensor on para-Sasakian manifolds. We prove that a quasi-conformally flat para-Sasakian manifold is an $ \eta $-Einstein manifold. Also, we give some results on the sectional curvature of such manifolds. Secondly, we consider the invariant submanifolds of a quasi-conformally flat para-Sasakian manifold. We prove that a totally umbilical submanifold of a para-Sasakian manifold is invariant. In addition, we investigate curvature properties of such submanifolds and we show that a totally umbilical invariant submanifold of a quasi-conformally flat para-Sasakian manifold is an $ \eta $-Einstein manifold. Finally, we work on the sectional curvature properties of an invariant submanifold of a quasi-conformally flat para-Sasakian manifold.

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Cite This Article

Ünal, İ., Sarı, R. (2020). On Quasi-Conformal Flat Para-Sasakian Manifolds. Turkish Journal of Mathematics and Computer Science, Volume: 12 Issue: 2. https://doi.org/10.47000/tjmcs.765297

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