References & Citations
Mathematics > Differential Geometry
Title: Real hypersurfaces in the complex projective plane satisfying an equality involving $δ(2)$
(Submitted on 4 May 2020 (v1), last revised 25 May 2021 (this version, v4))
Abstract: It was proved in Chen's paper \cite{chen} 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.
Submission history
From: Toru Sasahara [view email][v1] Mon, 4 May 2020 04:37:53 GMT (8kb)
[v2] Tue, 5 May 2020 09:31:24 GMT (8kb)
[v3] Wed, 31 Mar 2021 08:53:39 GMT (11kb)
[v4] Tue, 25 May 2021 10:43:01 GMT (12kb)
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