scholarly journals Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

2007 ◽  
Vol 75 (3) ◽  
pp. 563-581 ◽  
Author(s):  
N. Schmitt ◽  
M. Kilian ◽  
S.-P. Kobayashi ◽  
W. Rossman
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Dimensional Space ◽  
Space Forms ◽  
3 Dimensional

BONNET SURFACES IN FOUR-DIMENSIONAL SPACE FORMS

2004 ◽  
Vol 15 (10) ◽  
pp. 981-985
Author(s):  
ATSUSHI FUJIOKA
Keyword(s):  
Mean Curvature ◽  
Dimensional Space ◽  
Curvature Vector ◽  
Reduction Theorem ◽  
Mean Curvature Vector ◽  
Parallel Mean Curvature Vector ◽  
Space Forms ◽  
3 Dimensional ◽  
Flat Normal Bundle ◽  
Parallel Mean Curvature

We study isometric deformations of surfaces in four-dimensional space forms preserving the length of the mean curvature vector. In particular we consider the natural condition, called to be simple, and show that such surfaces with flat normal bundle are Bonnet surfaces in totally geodesic or umbilic 3-dimensional space forms, which is regarded as a generalization of Chen–Yau's reduction theorem for surfaces with parallel mean curvature vector.

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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