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For biharmonic maps, there is a famous conjecture named Chen's conjecture. Inlater paper, Wang and Ou gave an affirmative partial answer to submersionversion of Chen's conjecture. In this paper, we give an affirmative partialanswer to submersion version of generalized Chen's conjecture, that is,triharmonic Riemannian submersions from a 3-dimensional space form into asurface is harmonic.

Triharmonic Riemannian submersions from 3-dimensional manifolds of constant curvature