Minimal Surfaces with Constant Curvature in 4-Dimensional Space Forms

1983 ◽  
Vol 89 (1) ◽  
pp. 133 ◽  
Author(s):  
Katsuei Kenmotsu
Keyword(s):  
Constant Curvature ◽  
Minimal Surfaces ◽  
Dimensional Space ◽  
Space Forms

scholarly journals Transforms for minimal surfaces in 5-dimensional space forms

2017 ◽  
Vol 102 (116) ◽  
pp. 241-246 ◽  
Author(s):  
Makoto Sakaki
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Space Form ◽  
Dimensional Space ◽  
Space Forms

For a minimal surface in a 5-dimensional space form, we give transforms to get another minimal surface in another 5-or 4-dimensional space form.

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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