scholarly journals Classification of Lorentz surfaces with parallel mean curvature vector in non-flat pseudo-Riemannian space forms $S_2^4(1)$ and $H_2^4(-1)$

2013 ◽  
Vol 20 (4) ◽  
pp. 715-733
Author(s):  
Dan Yang ◽  
Yu Fu
Keyword(s):  
Mean Curvature ◽  
Riemannian Space ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Parallel Mean Curvature Vector ◽  
Space Forms ◽  
Parallel Mean Curvature ◽  
Riemannian Space Forms

scholarly journals Classification of f-biharmonic submanifolds in Lorentz space forms

2021 ◽  
Vol 19 (1) ◽  
pp. 1299-1314
Author(s):  
Li Du
Keyword(s):  
Vector Field ◽  
Mean Curvature ◽  
Lorentz Space ◽  
Curvature Vector ◽  
Shape Operator ◽  
Mean Curvature Vector ◽  
Biharmonic Submanifolds ◽  
Parallel Mean Curvature Vector ◽  
Space Forms ◽  
Parallel Mean Curvature

Abstract In this paper, f-biharmonic submanifolds with parallel normalized mean curvature vector field in Lorentz space forms are discussed. When f f 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 f f is a function, we completely classify such pseudo-umbilical submanifolds.

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