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arXiv · 2306.13910

$f$-Biharmonic submanifolds in space forms and $f$-biharmonic Riemannian submersions from 3-manifolds

Ze-Ping Wang·Li-Hua Qin
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Abstract

$f$-Biharmonic maps are generalizations of harmonic maps and biharmonic maps. In this paper, we obtain some descriptions of $f$-biharmonic curves in a space form. We also obtain a complete classification of proper $f$-biharmonic isometric immersions of a developable surface in $\r^3$ by proving that a proper $f$-biharmonic developable surface exists only in the case where the surface is a cylinder. Based on this, we show that a proper biharmonic conformal immersion of a developable surface into $\r^3$ exists only in the case when the surface is a cylinder. Riemannian submersions can be viewed as the dual notion of isometric immersions (i.e., submanifolds). We also study $f$-biharmonicity of Riemannian submersions from 3-space forms by using the integrability data. Examples are given of proper $f$-biharmonic Riemannian submersions and $f$-biharmonic surfaces and curves.

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Ze-Ping Wang, Li-Hua Qin. 2024-02-12. $f$-Biharmonic submanifolds in space forms and $f$-biharmonic Riemannian submersions from 3-manifolds. https://arxiv.org/abs/2306.13910

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