Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(6): 1651-1670

Online first article November 3, 2016      Printed November 30, 2016

https://doi.org/10.4134/BKMS.b150863

Copyright © The Korean Mathematical Society.

Some results of exponentially biharmonic maps into a non-positively curved manifold

Yingbo Han

Xinyang Normal University

Abstract

In this paper, we investigate exponentially biharmonic maps $u:(M,g)\rightarrow(N,h)$ from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that if \begin{align*} &\int_Me^{\frac{p|\tau(u)|^2}{2}}|\tau(u)|^{p}dv_g<\infty~(p\geq2),~\int_M|\tau(u)|^{2}dv_g<\infty\text{ and}\\ &\int_M|du|^{2}dv_g<\infty, \end{align*} then $u$ is harmonic. When $u$ is an isometric immersion, we get that if $\int_Me^{\frac{pm^2|H|^2}{2}}|H|^{q}dv_g<\infty$ for $2\leq p<\infty$ and $0

Keywords: exponentially biharmonic maps, exponentially biharmoinc submanifolds

MSC numbers: Primary 58E20, 53C21

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