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

Authors : T. SASAHARA

Pages : 305-312

Doi:10.36890/iejg.936026

View : 14 | Download : 8

Publication Date : 2021-10-29

Article Type : Research Paper

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 $$\deltainsert ignore into journalissuearticles values(2);\leq \frac{9}{4}H^2+5,$$ where $H$ is the mean curvature and $\deltainsert ignore into journalissuearticles values(2);$ 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