On real hypersurfaces in non-flat complex space forms with a condition on the structure Jacobi operator OPERATOR

TL;DR

This paper classifies real hypersurfaces in non-flat complex space forms based on conditions on the covariant derivative of the structure Jacobi operator and proves the non-existence of those with Codazzi type structure Jacobi operator.

Contribution

It provides new classification theorems for real hypersurfaces with specific Jacobi operator conditions and establishes non-existence results for Codazzi type cases.

Findings

Classification theorems for hypersurfaces with certain Jacobi operator conditions

Non-existence of hypersurfaces with Codazzi type structure Jacobi operator

Insights into the geometry of hypersurfaces in complex space forms

Abstract

In this paper we prove some classification theorems of real hypersur- faces in Mn(c) satisfying certain conditions on the covariant derivative of the structure Jacobi operator. We also prove the non-existence of real hypersurfaces with Codazzi type structure Jacobi operator in Mn(c).