Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME RESULTS OF f-BIHARMONIC MAPS INTO A RIEMANNIAN MANIFOLD OF NON-POSITIVE SECTIONAL CURVATURE

  • He, Guoqing (School of Science Nanjing University of Science and Technology) ;
  • Li, Jing (School of Science Nanjing University of Science and Technology) ;
  • Zhao, Peibiao (School of Science Nanjing University of Science and Technology)
  • Received : 2016.09.24
  • Accepted : 2017.06.21
  • Published : 2017.11.30
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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 $\int_{M}f^p{\mid}{\tau}(u){\mid}^pdv_g$ < ${\infty}$, $\int_{M}{\mid}{\tau}(u){\mid}^2dv_g$ < ${\infty}$ and $\int_{M}{\mid}du{\mid}^2dv_g$ < ${\infty}$, 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).

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References

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