Evolution of Ricci scalar under Finsler Ricci flow
B. Bidabad, M. K. Sedaghat,
2015.08.12
http://arxiv.org/abs/1508.03041
Recently, we have studied evolution of a family of Finsler metrics along
Finsler Ricci flow and proved its convergence in short time. Here, evolution
equation of the reduced $hh$curvature and the Ricci scalar along the
Finslerian Ricci flow is obtained and it is proved that the Ricci flow
preserves positivity of reduced $hh$curvature on finite time. Next, it is
shown that the evolution of Ricci scalar is a parabolictype equation and if
the initial Finsler metric is of positive flag curvature, then the flag
curvature and the Ricci scalar remain positive as long as the solution exists.
Finally, a lower bound for the Ricci scalar along the Ricci flow is obtained.
