Surfaces of constant curvature in 3-dimensional space forms

2009 ◽  
Vol 37 (1) ◽  
Author(s):  
José Gálvez
Keyword(s):  
Constant Curvature ◽  
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 The index of symmetry of three-dimensional Lie groups with a left-invariant metric

2018 ◽  
Vol 18 (4) ◽  
pp. 395-404 ◽  
Author(s):  
Silvio Reggiani
Keyword(s):  
Lie Groups ◽  
Constant Curvature ◽  
Lie Group ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Invariant Metric ◽  
3 Dimensional ◽  
Space Of Constant Curvature ◽  
Positive Index

Abstract We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive index of symmetry. We also study the geometry of the quotients by the so-called foliation of symmetry, and we explain in what cases the group fibers over a 2-dimensional space of constant curvature.

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
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