A Finsler manifold is said to be geodesically reversible if the reversed curve of any geodesic remains a geometrical geodesic. Well-known examples metrics are Randers with closed [Formula: see text]-forms. Another family well-known projectively flat on text]-sphere that have constant positive curvature. In this paper, we prove some and dynamical characterizations metrics, several rigidity resul...

We establish that Hitchin’s connection exist for any rigid holomorphic family of Kähler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove that Hitchin’s connection induces a unique formal connection on smooth functions on the symplectic manifold. Parallel transport of this formal connection pro...

The concept of locally dually flat Finsler metrics originate from information geometry. As we know, (α, β)-metrics defined by a Riemannian metric α and an 1-form β, represent an important class of Finsler metrics, which contains the Matsumoto metric. In this paper, we study and characterize locally dually flat first approximation of the Matsumoto metric with isotropic S-curvature, which is not ...

We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de–Rham sequence associated to a certain linear connection on the adjoint tractor bundle. For regular normal geometries, this description can be related to the underlying geometric structure using the machinery of BGG sequences. In the locally flat case...

A Finsler space (M,Σ) is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason [13], it is shown that a geodesically reversible Finsler metric of constant flag curvature on the...