scholarly journals On the uniqueness of complete biconservative surfaces in $3$-dimensional space forms

2021 ◽  
pp. 19
Author(s):  
Simona Nistor ◽  
Cezar Oniciuc
Keyword(s):  
Dimensional Space ◽  
Space Forms ◽  
3 Dimensional

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.

scholarly journals MANNHEIM CURVES IN 3-DIMENSIONAL SPACE FORMS

2013 ◽  
Vol 50 (4) ◽  
pp. 1099-1108 ◽  
Author(s):  
Jin Ho Choi ◽  
Tae Ho Kang ◽  
Young Ho Kim
Keyword(s):  
Dimensional Space ◽  
Space Forms ◽  
3 Dimensional

scholarly journals On biconservative surfaces in $3$-dimensional space forms

2016 ◽  
Vol 24 (5) ◽  
pp. 1027-1045 ◽  
Author(s):  
Dorel Fetcu ◽  
Simona Nistor ◽  
Cezar Oniciuc
Keyword(s):  
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.

scholarly journals A Note on Surfaces in Space Forms with Pythagorean Fundamental Forms

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 444
Author(s):  
Muhittin Evren Aydin ◽  
Adela Mihai
Keyword(s):  
Sectional Curvature ◽  
Present Note ◽  
Dimensional Space ◽  
Golden Ratio ◽  
Gauss Curvature ◽  
Constant Sectional Curvature ◽  
Round Sphere ◽  
Space Forms ◽  
Totally Umbilical ◽  
3 Dimensional

In the present note we introduce a Pythagorean-like formula for surfaces immersed into 3-dimensional space forms M 3 ( c ) of constant sectional curvature c = − 1 , 0 , 1 . More precisely, we consider a surface immersed into M 3 c satisfying I 2 + II 2 = III 2 , where I , II and III are the matrices corresponding to the first, second and third fundamental forms of the surface, respectively. We prove that such a surface is a totally umbilical round sphere with Gauss curvature φ + c , where φ is the Golden ratio.

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