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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2020 / Volume: 69 Issue: 2

Invariant submanifolds in golden Riemannian manifolds

Erol Kılıç(İnönü Üniversitesi)0000-0001-7536-0404
Mustafa Gök(İNÖNÜ ÜNİVERSİTESİ)0000-0001-6346-0758
Sadık Keleş(İnönü Üniversitesi)0000-0003-3981-2092
Pages
—
Publication Date
2020-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we present an example of an invariant submanifold.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study invariant submanifolds of a golden Riemannian manifold with the aid of induced structures on them by the golden structure of the ambient manifold.
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Key Findings & Data:We demonstrate that any invariant submanifold in a locally decomposable golden Riemannian manifold leaves invariant the locally decomposability of the ambient manifold.
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Conclusion & Impact:Finally, we present an example of an invariant submanifold.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Invariant Submanifold · Golden Structure · Golden Riemannian Manifold

Abstract

In this paper, we study invariant submanifolds of a golden Riemannian manifold with the aid of induced structures on them by the golden structure of the ambient manifold. We demonstrate that any invariant submanifold in a locally decomposable golden Riemannian manifold leaves invariant the locally decomposability of the ambient manifold. We give a necessary and sufficient condition for any submanifold in a golden Riemannian manifold to be invariant. We obtain some necessary conditions for the totally geodesicity of invariant submanifolds. Moreover, we find some facts on invariant submanifolds. Finally, we present an example of an invariant submanifold.

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Cite This Article

Kılıç, E., Gök, M., Keleş, S. (2020). Invariant submanifolds in golden Riemannian manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 2. https://doi.org/10.31801/cfsuasmas.635434

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