2015/08/12 by Behroz Bidabad, B. Bidabad, Bidabad, B. +2
Mathematics · Physics and Astronomy · #53C44 #53C60 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG #msc:53C44 #msc:53C60
paper · pdf · doi:10.48550/arxiv.1508.03041
17 pages. arXiv admin note: text overlap with arXiv:1508.02893
arxiv created 2015/08/12 · openalex publication_date 2015/08/12 · arxiv updated 2015/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 parabolic-type 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.