Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$

Year 2021, Volume: 14 Issue: 2, 305 - 312, 29.10.2021

T. Sasahara

https://doi.org/10.36890/iejg.936026

Cited By: 1

Abstract

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.

Keywords

Real hypersurfaces, ruled, δ(2)-ideal, complex projective plane

References

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