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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.
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참고문헌 (15)
참고문헌 신청
H. Akbar-Zadeh / 2006 / Initiation to Global Finslerian Geometry, North-Holland Mathematical Library, 68 / Elsevier Science B.V.
S. Azami / 2013 / Existence and uniqueness for solution of Ricci flow on Finsler manifolds / Int. J. Geom. Methods Mod. Phys. 10(3):21
D. Bao / 2007 / Finsler geometry, Sapporo 2005-in memory of Makoto Matsumoto / Math. Soc. Japan :19~71
D. Bao / 2000 / An Introduction to Riemann-Finsler Geometry, Graduate Texts in Mathematics, 200 / Springer-Verlag
D. Bao / 1994 / On the volume of unit tangent spheres in a Finsler manifold / Results Math. 26(1-2):1~17
S. Azami / 2013 / Existence and uniqueness for solution of Ricci flow on Finsler manifolds / Int. J. Geom. Methods Mod. Phys. 10(3):21
D. Bao / 2007 / Finsler geometry, Sapporo 2005-in memory of Makoto Matsumoto / Math. Soc. Japan :19~71
D. Bao / 2000 / An Introduction to Riemann-Finsler Geometry, Graduate Texts in Mathematics, 200 / Springer-Verlag
D. Bao / 1994 / On the volume of unit tangent spheres in a Finsler manifold / Results Math. 26(1-2):1~17
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