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 Biharmonic pseudo-Riemannian submersions from 3-manifolds

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 543-552
Author(s):  
İrem Erken ◽  
Cengizhan Murathan
Keyword(s):  
Space Form ◽  
Dimensional Space ◽  
Riemannian Submersions ◽  
3 Dimensional

We classify the pseudo-Riemannian biharmonic submersion from a 3-dimensional space form onto a surface.

scholarly journals Complete surfaces in 3-dimensional space forms

1972 ◽  
Vol 1 (2) ◽  
pp. 275-279
Author(s):  
Takehiro ITOH
Keyword(s):  
Dimensional Space ◽  
Space Forms ◽  
3 Dimensional ◽  
Complete Surfaces

scholarly journals Harmonic morphisms and conformal foliations by geodesics of three-dimensional space forms

1991 ◽  
Vol 51 (1) ◽  
pp. 118-153 ◽  
Author(s):  
Paul Baird ◽  
John C. Wood
Keyword(s):  
Space Form ◽  
Holomorphic Mapping ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Classification ◽  
Harmonic Morphisms ◽  
Connected Space ◽  
Space Forms ◽  
Simply Connected ◽  
Three Dimensional Space

AbstractA complete classification is given of harmonic morphisms to a surface and conformal foliations by geodesics, with or without isolated singularities, of a simply-connected space form. The method is to associate to any such a holomorphic map from a Riemann surface into the space of geodesics of the space form. Properties such as nonintersecting fibres (or leaves) are translated into conditions on the holomorphic mapping which show it must have a simple form corresponding to a standard example.

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

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

scholarly journals On 3-dimensional contact slant submanifolds in Sasakian space forms

2003 ◽  
Vol 68 (2) ◽  
pp. 275-283 ◽  
Author(s):  
Ion Mihai ◽  
Yoshihiko Tazawa
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Sharp Inequality ◽  
Sasakian Space Form ◽  
Slant Submanifold ◽  
Space Forms ◽  
3 Dimensional ◽  
Slant Submanifolds ◽  
Sasakian Space Forms ◽  
Complex Space Forms

Recently, B.-Y. Chen obtained an inequality for slant surfaces in complex space forms. Further, B.-Y. Chen and one of the present authors proved the non-minimality of proper slant surfaces in non-flat complex space forms. In the present paper, we investigate 3-dimensional proper contact slant submanifolds in Sasakian space forms. A sharp inequality is obtained between the scalar curvature (intrinsic invariant) and the main extrinsic invariant, namely the squared mean curvature.It is also shown that a 3-dimensional contact slant submanifold M of a Sasakian space form M̆(c), with c ≠ 1, cannot be minimal.

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