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ON EVOLUTION OF FINSLER RICCI SCALAR
Bidabad, Behroz,Sedaghat, Maral Khadem Korean Mathematical Society 2018 대한수학회지 Vol.55 No.3
Here, we calculate the evolution equation of the reduced hh-curvature and the Ricci scalar along the Finslerian Ricci flow. We prove that Finsler Ricci flow preserves positivity of the reduced hh-curvature on finite time. Next, it is shown that evolution of Ricci scalar is a parabolic-type equation and moreover if the initial Finsler metric is of positive flag curvature, then the flag curvature, as well as the Ricci scalar, remain positive as long as the solution exists. Finally, we present a lower bound for Ricci scalar along Ricci flow.
On evolution of Finsler Ricci scalar
Behroz Bidabad,Maral Khadem Sedaghat 대한수학회 2018 대한수학회지 Vol.55 No.3
Here, we calculate the evolution equation of the reduced $hh$-curvature and the Ricci scalar along the Finslerian Ricci flow. We prove that Finsler Ricci flow preserves positivity of the reduced $hh$-curvature on finite time. Next, it is shown that evolution of Ricci scalar is a parabolic-type equation and moreover if the initial Finsler metric is of positive flag curvature, then the flag curvature, as well as the Ricci scalar, remain positive as long as the solution exists. Finally, we present a lower bound for Ricci scalar along Ricci flow.