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Journals / Turkish Journal of Mathematics and Computer Science / 2019 / Cilt: 11 - Sayı: 1

On Submanifolds in a Riemannian Manifold with Golden Structure

Mobin AHMAD
Mohammad Aamir QAYYOOM
Pages
8–23
DOI
—
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AI Summary & Key Takeaways

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

We also construct an example on submanifold of a golden Riemannian manifold.

📌 3 Key Takeaways

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Objective & Hypothesis:A golden Riemannian structure $(J,g)$ on a Riemannian manifold is given by a tensor field $J$ of type $(1,1)$ satisfying the golden section relation $J^{2}=J+I,$ and a pure Riemannian metric $g$, that is a metric satisfying $g(JX,Y)=g(X,JY).$ We investigate some fundamental properties of the induced structure on submanifolds immersed in golden Riemannian manifolds.
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Key Findings & Data:We obtain effective relations for some induced structures on submanifolds of codimension 2.
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Conclusion & Impact:We also construct an example on submanifold of a golden Riemannian manifold.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Golden structure · Riemannian manifold · totally geodesics

Abstract

A golden Riemannian structure $(J,g)$ on a Riemannian manifold is given by a tensor field $J$ of type $(1,1)$ satisfying the golden section relation $J^{2}=J+I,$ and a pure Riemannian metric $g$, that is a metric satisfying $g(JX,Y)=g(X,JY).$ We investigate some fundamental properties of the induced structure on submanifolds immersed in golden Riemannian manifolds. We obtain effective relations for some induced structures on submanifolds of codimension 2. We also construct an example on submanifold of a golden Riemannian manifold.

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Cite This Article

AHMAD, M., QAYYOOM, M. A. (2019). On Submanifolds in a Riemannian Manifold with Golden Structure. Turkish Journal of Mathematics and Computer Science, Cilt: 11 - Sayı: 1, 8–23. https://ajindex.com/articles/374658

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References (2)

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