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http://dx.doi.org/10.4134/BKMS.b160780

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.6, 2017 , pp. 2119-2139 More about this Journal
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.
Keywords
deformation; Finsler Ricci flow; blow up; evolution; heat-type equation;
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