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Triharmonic Riemannian submersions from 3-dimensional space forms
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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.
Title: Triharmonic Riemannian submersions from 3-dimensional space forms
Description:
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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