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Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 2

Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving δ(2)

TORU SASAHARA
Pages
305–312
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

We describe how to obtain all such hypersurfaces.

📌 3 Key Takeaways

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Objective & Hypothesis:It was proved in Chen’s paper (Arch.
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Key Findings & Data:Math. (Basel) 67 (1996), 519–528) that every real hypersurface in the complex projective plane of constant holomorphic sectional curvature 4 satisfies δ(2) ≤ 9 4 H2 + 5, where H is the mean curvature and δ(2) is a δ-invariant introduced by him.
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Conclusion & Impact:We describe how to obtain all such hypersurfaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

It was proved in Chen’s paper (Arch. Math. (Basel) 67 (1996), 519–528) that every real hypersurface in the complex projective plane of constant holomorphic sectional curvature 4 satisfies δ(2) ≤ 9 4 H2 + 5, where H is the mean curvature and δ(2) is a δ-invariant introduced by him. In this paper, we study non-Hopf real hypersurfaces satisfying the equality case of the inequality under the condition that the mean curvature is constant along each integral curve of the Reeb vector field. We describe how to obtain all such hypersurfaces.

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Cite This Article

SASAHARA, T. (2022). Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving δ(2). International Electronic Journal of Geometry, Cilt: 14 - Sayı: 2, 305–312. https://ajindex.com/articles/539579

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References (7)

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  3. Chen, B. Y.: A general inequality for submanifolds in complex space forms and its applications. Arch. Math. (Basel) 67, 519–528 (1996)
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  7. Sasahara, T.: Real hypersurfaces in the complex projective plane attaining equality in a basic inequality. Houston J. Math. 43, 89-94 (2017)