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Journals / Turkish Journal of Mathematics and Computer Science / 2020 / Cilt: 12 - Sayı: 2

On Quasi-Conformal Flat Para-Sasakian Manifolds

Ramazan SARI
İnan ÜNAL
Pages
86–91
Publication Date
2022-11-04
DOI
—
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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

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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
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⚙️Variables:Domain Parameters

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

SARI, R., ÜNAL, İ. (2022). On Quasi-Conformal Flat Para-Sasakian Manifolds. Turkish Journal of Mathematics and Computer Science, Cilt: 12 - Sayı: 2, 86–91. https://ajindex.com/articles/609118

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