Finslerian geodesics on Fréchet manifolds

Biharmonic curves in Finsler spaces

Biharmonic curves are a generalization of geodesics, with applications in elasticity theory and various branches of computer science. The paper proposes a first study of biharmonic curves in spaces with Finslerian geometry, covering the following topics: a deduction of their equations, existence of non-geodesic biharmonic curves for some classes of Finsler spaces and specific properties. We prove, for instance, that geodesic curvature is constant along Finslerian biharmonic curves. Integration of the biharmonic equation is presented for two concrete Finsler metrics.

A note on the Sagnac effect in general relativity as a Finslerian effect

The geometry of the Sagnac effect in a stationary region of a spacetime is reviewed with the aim of emphasizing the role of asymmetry of a Finsler metric defined on a spacelike hypersurface associated to a stationary splitting and related to future-pointing null geodesics of the spacetime. We show also that an analogous asymmetry comes into play in the Sagnac effect for timelike geodesics.

Isometries, submetries and distance coordinates on Finsler manifolds

This paper considers fundamental issues related to Finslerian isometries, submetries, distance and geodesics. It is shown that at each point of a Finsler manifold there is a distance coordinate system. Using distance coordinates, a simple proof is given for the Finslerian version of the Myers-Steenrod theorem and for the differentiability of Finslerian submetries.

芬斯勒光凸边界：在因果简单性与锥测地线空间 $\mathcal{N}$ 中的应用

Finslerian lightconvex boundaries: applications to causal simplicity and the space of cone geodesics $\mathcal{N}$

本文研究带边界的非定芬斯勒流形和锥结构，证明边界光凸性、内部因果简单性与锥测地线空间豪斯多夫性三者等价，并显式构造锥测地线空间的流形结构，推广了渐近 AdS 时空等应用。

Filling minimality of Finslerian 2-discs

We prove that every Riemannian metric on the 2-disc such that all its geodesics are minimal, is a minimal filling of its boundary (within the class of fillings homeomorphic to the disc). This improves an earlier result of the author by removing the assumption that the boundary is convex. More generally, we prove this result for Finsler metrics with area defined as the two-dimensional Holmes-Thompson volume. This implies a generalization of Pu's isosystolic inequality to Finsler metrics, both for Holmes-Thompson and Busemann definitions of Finsler area.

The tangent bundle exponential map and locally autoparallel coordinates for general connections with application to Finslerian geometries

We construct a tangent bundle exponential map and locally autoparallel coordinates for geometries based on a general connection on the tangent bundle of a manifold. As concrete application we use these new coordinates for Finslerian geometries and obtain Finslerian geodesic coordinates. They generalise normal coordinates known from metric geometry to Finsler geometric manifolds and it turns out that they are identical to the Douglas-Thomas normal coordinates introduced earlier. We expand the fundamental geometry function of a Finsler spacetime in these new coordinates and find that it is const…