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Journals / International Electronic Journal of Geometry / 2019 / Cilt: 12 - Sayı: 1

Estimates of B.-Y. Chen’s ^ -Invariant in Terms of Casorati Curvature and Mean Curvature for Strictly Convex Euclidean Hypersurfaces

Mihaela B. VAJİAC
Bogdan D. SUCEAVA
Pages
26–31
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

As a consequence, we obtain anew string of inequalities in the geometry of strictly convex smooth hypersurfaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Chen’s ^-invariants can be estimated in function of other curvature terms through an algebraicprocess using the AM-GM and AM-QM inequalities.
📊
Key Findings & Data:This procedure works on strictly convexsmooth hypersurfaces lying in an Euclidean ambient space, and the estimates relate some ^-invariants to Germain’s mean curvature and Casorati curvature.
💡
Conclusion & Impact:As a consequence, we obtain anew string of inequalities in the geometry of strictly convex smooth hypersurfaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

B.-Y. Chen’s ^-invariants can be estimated in function of other curvature terms through an algebraicprocess using the AM-GM and AM-QM inequalities. This procedure works on strictly convexsmooth hypersurfaces lying in an Euclidean ambient space, and the estimates relate some ^-invariants to Germain’s mean curvature and Casorati curvature. As a consequence, we obtain anew string of inequalities in the geometry of strictly convex smooth hypersurfaces.

🔖

Cite This Article

VAJİAC, M. B., SUCEAVA, B. D. (2022). Estimates of B.-Y. Chen’s ^ -Invariant in Terms of Casorati Curvature and Mean Curvature for Strictly Convex Euclidean Hypersurfaces. International Electronic Journal of Geometry, Cilt: 12 - Sayı: 1, 26–31. https://ajindex.com/articles/539638

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