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Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 1

Some Results on Statistical Hypersurfaces of Sasakian Statistical Manifolds and Holomorphic Statistical Manifolds

Feng WU
Yan JİANG
Liang ZHANG
Pages
46–58
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

Moreover, we construct several examples of statistical manifolds, Sasakian statistical manifolds and holomorphic statistical manifolds of constant holomorphic curvature zero.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the statistical immersion of codimension one from a Sasakian statistical manifold of constant φ− curvature to a holomorphic statistical manifold of constant holomorphic curvature and its converse.
📊
Key Findings & Data:We prove that in both cases the constant φ− curvature equals to one and the constant holomorphic curvature must be zero.
💡
Conclusion & Impact:Moreover, we construct several examples of statistical manifolds, Sasakian statistical manifolds and holomorphic statistical manifolds of constant holomorphic curvature zero.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sasakian statistical manifolds · holomorphic statistical manifolds · constant φ−curvature

Abstract

In this paper, we study the statistical immersion of codimension one from a Sasakian statistical manifold of constant φ− curvature to a holomorphic statistical manifold of constant holomorphic curvature and its converse. We prove that in both cases the constant φ− curvature equals to one and the constant holomorphic curvature must be zero. Moreover, we construct several examples of statistical manifolds, Sasakian statistical manifolds and holomorphic statistical manifolds of constant holomorphic curvature zero.

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Cite This Article

WU, F., JİANG, Y., ZHANG, L. (2022). Some Results on Statistical Hypersurfaces of Sasakian Statistical Manifolds and Holomorphic Statistical Manifolds. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 46–58. https://ajindex.com/articles/539589

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