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DEFORMATION OF CARTAN CURVATURE ON FINSLER MANIFOLDS
Bidabad, Behroz,Shahi, Alireza,Ahmadi, Mohamad Yar Korean Mathematical Society 2017 대한수학회보 Vol.54 No.6
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.
Deformation of Cartan curvature on Finsler manifolds
Behroz Bidabad,Alireza Shahi,Mohamad Yar Ahmadi 대한수학회 2017 대한수학회보 Vol.54 No.6
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.