Bull. Korean Math. Soc. 2017; 54(6): 2091-2106
Online first article July 26, 2017 Printed November 30, 2017
https://doi.org/10.4134/BKMS.b160773
Copyright © The Korean Mathematical Society.
Guoqing He, Jing Li, Peibiao Zhao
AnHui Normal University, Nanjing University of Science and Technology, Nanjing University of Science and Technology
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
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd