Finsler spaces admitting a parallel vector field.
The aim of this paper is to construct a canonical nonlinear connection on the 1-jet space from the Euler-Lagrange equations of the quadratic multi-time Lagrangian function
The Bott-Chern cohomology groups and the Bott-Chern Laplacian on differential forms of mixed type on a compact foliated Kähler manifold are defined and studied. Also, a Hodge decomposition theorem of Bott-Chern type for differential forms of mixed type is proved. Finally, the case of projectivized tangent bundle of a complex Finsler manifold is discussed.
In this paper we study isometry-invariant Finsler metrics on inner product spaces over or , i.e. the Finsler metrics which do not change under the action of all isometries of the inner product space. We give a new proof of the analytic description of all such metrics. In this article the most general concept of the Finsler metric is considered without any additional assumptions that are usually built into its definition. However, we present refined versions of the described results for more specific...