Some results of $f$-biharmonic maps into a Riemannian manifold of non-positive sectional curvature
Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 2091-2106
Published online November 30, 2017
Guoqing He, Jing Li, Peibiao Zhao
AnHui Normal University, Nanjing University of Science and Technology, Nanjing University of Science and Technology
Abstract : The authors investigate $f$-biharmonic maps $u: (M,g)\rightarrow(N,h)$ from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature, and derive that if $\int_{M}f^{p}|\tau(u)|^{p}dv_{g}<\infty$, $\int_{M}|\tau(u)|^{2}dv_{g}<\infty$ and $\int_{M}|du|^{2}dv_{g}<\infty$, then $u$ is harmonic. When $u$ is an isometric immersion, the authors also get that if $u$ satisfies some integral conditions, then it is minimal. These results give an affirmative partial answer to conjecture 4 (generalized Chen's conjecture for $f$-biharmonic submanifolds).
Keywords : $f$-biharmonic maps, $f$-biharmonic submanifolds
MSC numbers : 58E20, 53C21
Downloads: Full-text PDF  

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail:   | Powered by INFOrang Co., Ltd