Yamabe Problem on Finsler Manifolds

Yamabe Problem on Finsler Manifolds

In this paper, we study conformal deformations and C-conformal deformations of Ricci- directional and second type scalar curvture of Finsler manifolds. After that, the critical points of Akbar-Zadeh functional are found in two situations. Based on the constant Indi- catrix volume and restricting its variations to the point-wise conformal transformations, we prove that the critical points of functional are metrics of constant Ricci-directional curvature. Next, Finslerian functional is introduced and show that Akbar-Zadeh curvature functional is the example of Finslerian functional. And nally, Yamabe functional and Yamabe ow on Finsler manifolds are introduced.