Tohoku Mathematical Journal
2021
March
SECOND SERIES VOL. 73, NO. 1

Tohoku Math. J.
73 (2021), 39-48

Title FINSLER CONFORMAL CHANGES PRESERVING THE MODIFIED RICCI CURVATURE

Author Bin Chen and Lili Zhao

(Received June 7, 2019)
Abstract. On a Riemannian manifold, a Liouville transformation is a conformal change which preserves the Ricci tensor. In Finsler geometry, there are various types of Ricci curvature. By adding a Landsberg curvature term to the classical Ricci curvature, we consider the conformal transformations on a Finsler manifold such that this modified Ricci curvature is preserved. We prove that such conformal transformations are homothetic if the space is C-convex. The conformal rigidity for Landsberg surfaces is also obtained.

Mathematics Subject Classification. Primary 53C60; Secondary 53B40.
Key words and phrases. Finsler metrics, Ricci curvature, Liouville transformation.

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