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.

中文翻译：

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来自三维空间形式的三谐波黎曼浸入式

我们表明，从3维空间形式到表面的任何三次谐波黎曼浸没都是谐波。这是对广义Chen猜想的浸没版本的肯定的部分答案。此外，还提出了f-双调和黎曼浸入式的不存在性定理。