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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 5

Metallic Riemannian space forms

Metalik Riemann uzay form

Fulya Şahin(EGE ÜNİVERSİTESİ)0000-0002-3383-092X
Bayram Şahin(EGE UNIVERSITY)0000-0002-9372-1151
Feyza Esra Erdoğan(Ege University)0000-0003-0568-7510
Pages
—
Publication Date
2026-10-28
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AI Summary & Key Takeaways

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

Finally, this new curvature notion is applied to semi-invariant and totally umbilical submanifolds, yielding rich geometric results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study we examine the cases of constant sectional curvature in Metallic Riemannian manifolds.
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Key Findings & Data:We show that classical and holomorphic-like curvatures generally make the manifold flat.
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Conclusion & Impact:Finally, this new curvature notion is applied to semi-invariant and totally umbilical submanifolds, yielding rich geometric results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Metallic Riemannian manifold · sectional curvature · space form

Abstract

In this study we examine the cases of constant sectional curvature in Metallic Riemannian manifolds. We show that classical and holomorphic-like curvatures generally make the manifold flat. Based on this, we introduce a new concept called Metallic sectional curvature, and in this setting, we derive the explicit expression of the curvature tensor. In addition, the Ricci tensor and scalar curvature are computed, and the conditions under which the manifold is Einstein are discussed. Finally, this new curvature notion is applied to semi-invariant and totally umbilical submanifolds, yielding rich geometric results.

Özet

Bu çalışmada, Metalik Riemannian manifoldlarda sabit kesit eğriliği durumlarını inceliyoruz. Klasik ve holomorfik-benzeri eğriliklerin, genel olarak manifoldun düz (flat) olmasına yol açtığını gösteriyoruz. Buna dayanarak, **Metalik kesit eğriliği** adı verilen yeni bir kavram tanıtıyoruz ve bu çerçevede eğrilik tensörünün açık ifadesini elde ediyoruz. Ayrıca, Ricci tensörü ve skaler eğrilik hesaplanmakta ve manifoldun hangi koşullar altında Einstein olduğu tartışılmaktadır. Son olarak, bu yeni eğrilik kavramı yarı-invariant ve tam umbilical altmanifoldlara uygulanarak zengin geometrik sonuçlara ulaşılmaktadır.

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Cite This Article

Şahin, F., Şahin, B., Erdoğan, F. E. (2026). Metallic Riemannian space forms. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 5. https://doi.org/10.15672/hujms.1829922

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