Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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VANISHING PROPERTIES OF p-HARMONIC ℓ-FORMS ON RIEMANNIAN MANIFOLDS

  • Nguyen, Thac Dung (Department of Mathematics Mechanics and Informatics College of Science Viet Nam National University) ;
  • Pham, Trong Tien (Department of Mathematics Mechanics and Informatics College of Science Viet Nam National University)
  • Received : 2017.09.04
  • Accepted : 2018.06.07
  • Published : 2018.09.01
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Abstract

In this paper, we show several vanishing type theorems for p-harmonic ${\ell}$-forms on Riemannian manifolds ($p{\geq}2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of $N^{n+m}$ with flat normal bundle, we prove that any p-harmonic ${\ell}$-form on M is trivial if N has pure curvature tensor and M satisfies some geometric conditions. Then, we obtain a vanishing theorem on Riemannian manifolds with a weighted $Poincar{\acute{e}}$ inequality. Final, we investigate complete simply connected, locally conformally flat Riemannian manifolds M and point out that there is no nontrivial p-harmonic ${\ell}$-form on M provided that the Ricci curvature has suitable bound.

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Acknowledgement

Supported by : NAFOSTED

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