Classification of f-biharmonic submanifolds in Lorentz space forms

Abstract

In this paper, f-biharmonic submanifolds with parallel normalized mean curvature vector field in Lorentz space forms are discussed. When ff is a constant, we prove that such submanifolds have parallel mean curvature vector field with the minimal polynomial of the shape operator of degree ≤2\le 2. When ff is a function, we completely classify such pseudo-umbilical submanifolds.

Keywords

• lorentz space forms
• f-biharmonic submanifolds
• parallel normal mean curvature vector field
• the shape operator
• pseudo-umbilical
• 53c40