Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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DEFORMATION OF CARTAN CURVATURE ON FINSLER MANIFOLDS

  • Bidabad, Behroz (Faculty of Mathematics and Computer Science Amirkabir University of Technology) ;
  • Shahi, Alireza (Faculty of Mathematics and Computer Science Amirkabir University of Technology) ;
  • Ahmadi, Mohamad Yar (Faculty of Mathematics and Computer Science Amirkabir University of Technology)
  • Received : 2016.09.28
  • Accepted : 2017.03.14
  • Published : 2017.11.30
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Abstract

Here, certain Ricci flow for Finsler n-manifolds is considered and deformation of Cartan hh-curvature, as well as Ricci tensor and scalar curvature, are derived for spaces of scalar flag curvature. As an application, it is shown that on a family of Finsler manifolds of constant flag curvature, the scalar curvature satisfies the so-called heat-type equation. Hence on a compact Finsler manifold of constant flag curvature of initial non-negative scalar curvature, the scalar curvature remains non-negative by Ricci flow and blows up in a short time.

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References

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