Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$
| Autor: | Toru Sasahara |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
Matematik Pure mathematics Mean curvature Applied Mathematics Holomorphic function Integral curve Hypersurface Real hypersurfaces ruled δ(2)-ideal complex projective plane Reeb vector field Mathematics::Differential Geometry Geometry and Topology Sectional curvature Constant (mathematics) Mathematics Mathematical Physics Complex projective plane |
| Zdroj: | Volume: 14, Issue: 2 305-312 International Electronic Journal of Geometry |
| ISSN: | 1307-5624 |
| DOI: | 10.36890/iejg.936026 |
| Popis: | It was proved in Chen's paper [3] that every real hypersurface in the complex projective plane of constant holomorphic sectional curvature $4$ satisfies $$\delta(2)\leq \frac{9}{4}H^2+5,$$ where $H$ is the mean curvature and $\delta(2)$ is a $\delta$-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. |
| Databáze: | OpenAIRE |
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