scholarly journals f-Biharmonic Submanifolds of Generalized Space Forms

2019 ◽  
Vol 75 (1) ◽  
Author(s):  
Julien Roth ◽  
Abhitosh Upadhyay
Keyword(s):  
Biharmonic Submanifolds ◽  
Space Forms

scholarly journals BIHARMONIC SUBMANIFOLDS IN NONFLAT LORENTZ 3-SPACE FORMS

2011 ◽  
Vol 85 (3) ◽  
pp. 422-432 ◽  
Author(s):  
TORU SASAHARA
Keyword(s):  
Biharmonic Submanifolds ◽  
De Sitter ◽  
Space Forms ◽  
Curves And Surfaces ◽  
Biharmonic Curves

AbstractThe purpose of this paper is to classify nonharmonic biharmonic curves and surfaces in de Sitter 3-space and anti-de Sitter 3-space.

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.

Triharmonic Riemannian submersions from 3-dimensional space forms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tomoya Miura ◽  
Shun Maeta
Keyword(s):  
Existence Theorem ◽  
Space Form ◽  
Dimensional Space ◽  
Riemannian Submersion ◽  
Partial Answer ◽  
Riemannian Submersions ◽  
Space Forms ◽  
3 Dimensional

Abstract We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.

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