Triharmonic Riemannian submersions from 3-dimensional manifolds of constant curvature

2016/08/22 by Miura, Tomoya, Maeta, Shun
#Differential Geometry (math.DG) #FOS: Mathematics #primary 58E20 #secondary 53C43

paper · doi:10.48550/arxiv.1608.06088

Abstract

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

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