Real hypersurfaces in the complex projective plane satisfying an equality involving δ(2)

2020/05/04 by Toru Sasahara, Sasahara, Toru
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2005.01266

openalex publication_date 2020/05/04 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28

Abstract

It was proved in Chen's paper \citechen 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.

Related

• Real hypersurfaces in the complex projective plane attaining equality in a basic inequality
• Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane
• On complete hypersurfaces with constant mean and scalar curvatures in Euclidean spaces
• Non-Hopf real hypersurfaces with constant principal curvatures in complex space forms
• Real hypersurfaces in complex space forms attaining equality in an inequality involving a contact δ-invariant