Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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RIGIDITY THEOREMS OF SOME DUALLY FLAT FINSLER METRICS AND ITS APPLICATIONS

  • Shen, Bin (Department of Mathematics Southeast University) ;
  • Tian, Yanfang (Logistical Engineering University of PLA)
  • Received : 2015.09.17
  • Published : 2016.09.30
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Abstract

In this paper, we study a class of Finsler metric. First, we find some rigidity results of the dually flat (${\alpha}$, ${\beta}$)-metric where the underline Riemannian metric ${\alpha}$ satisfies nonnegative curvature properties. We give a new geometric approach of the Monge-$Amp{\acute{e}}re$ type equation on $R^n$ by using those results. We also get the non-existence of the compact globally dually flat Riemannian manifold.

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Acknowledgement

Supported by : Central Universities, Natural Science Foundation of Jiangsu Province, NSFC

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