Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving δ(2)

被引：2

作者：

Sasahara, Toru ^{[1
]}

机构：

[1] Hachinohe Inst Technol, Ctr Liberal Arts & Sci, Hachinohe, Aomori 0318501, Japan

来源：

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY | 2021年 / 14卷 / 02期

关键词：

Real hypersurfaces; ruled; delta(2)-ideal; complex projective plane;

D O I：

10.36890/IEJG.936026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It was proved in Chen's paper (Arch. Math. (Basel) 67 (1996), 519-528) that every real hypersurfacein the complex projective plane of constant holomorphic sectional curvature 4 satisfies delta(2) <= 9/4 H-2 + 5, where His 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.

引用

页码：305 / 312

页数：8

共 7 条

[1]

Cecil TE, 2015, SPRINGER MONOGR MATH, P1, DOI 10.1007/978-1-4939-3246-7

[2]

Chen B.Y., 2011, Pseudo-Riemannian Geometry, -invariants and Applications

[3] SOME PINCHING AND CLASSIFICATION-THEOREMS FOR MINIMAL SUBMANIFOLDS [J].