Generalized Chen's Conjecture for Biharmonic Maps on Foliations

Xueshan Fu; Seoung Dal Jung*

doi:10.5666/KMJ.2023.63.4.593

Article

Kyungpook Mathematical Journal 2023; 63(4): 593-610

Published online December 31, 2023

Generalized Chen's Conjecture for Biharmonic Maps on Foliations

Xueshan Fu, Seoung Dal Jung*

Department of Mathematics, Shenyang University of Technology, Shenyang 110870, People Republic of China
e-mail : xsfu@sut.edu.cn

Department of Mathematics, Jeju National University, Jeju 63243, Republic of Korea
e-mail : sdjung@jejunu.ac.kr

Received: August 31, 2023; Accepted: November 3, 2023

Abstract

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Abstract

In this paper, we prove the generalized Chen's conjecture for (F,F′)-biharmonic maps, such maps are critical points of the transversal bienergy functional.

Keywords: Riemannian foliation, Transversally harmonic map, Transversally biharmonic map, (F,F′)&am