Journal ArticleDOI
Finsler Metrics with K= 0 and S= 0
TLDR
In this article, the shortest-time problem on a Riemannian space with an external force was studied, and it was shown that the problem can be converted to a shortest path problem on the Randers space.Abstract:
In the paper, we study the shortest time problem on a Riemannian space with an external force. We show that such problem can be converted to a shortest path problem on a Randers space. By choosing an appropriate external force on the Euclidean space, we obtain a non-trivial Randers metric of zero flag curvature. We also show that any positively complete Randers metric with zero flag curvature must be locally Minkowskian.read more
Citations
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Journal ArticleDOI
Zermelo navigation on Riemannian manifolds
TL;DR: In this paper, the authors studied Zermelo navigation on Riemannian manifolds and used that to solve a long standing problem in Finsler geometry, namely the complete classification of strongly convex Randers metrics of constant flag curvature.
Journal ArticleDOI
Riemann–Finsler geometry and Lorentz-violating kinematics
TL;DR: In this paper, an effective field theory with explicit Lorentz violation is constructed from a 1-form coefficient and has a Finsler structure complementary to the Randers structure.
Journal ArticleDOI
Stationary metrics and optical Zermelo-Randers-Finsler geometry
TL;DR: In this article, the authors consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field.
Book
Homogeneous Finsler Spaces
TL;DR: In this article, the authors studied homogeneous Finsler spaces of negative curvature and proved that every homogeneous manifold with non-positive flag curvatures and negative Ricci scalar must be connected.
Journal ArticleDOI
Projectively flat Finsler metrics of constant flag curvature
TL;DR: In this paper, the authors discuss the classification problem of projective Finsler metrics with constant flag curvatures, which they express by a Taylor expansion or an algebraic formula.
References
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Book
An Introduction to Riemann-Finsler Geometry
TL;DR: In this paper, the authors introduce the concept of Finsler Manifolds and the fundamental properties of Minkowski Norms, and present an interesting family of examples of these properties.
Book
Lectures on finsler geometry
TL;DR: Finsler Spaces Finsler m Spaces Co-area Formula Isoperimetric Inequalities Geodesics and Connection Riemann Curvature Non-Riemannian Curvatures Structure Equations as discussed by the authors.
Journal ArticleDOI
On an Asymmetrical Metric in the Four-Space of General Relativity
TL;DR: In this article, the simplest possible asymmetrical generalization of Riemannian metric is considered, and the physical consequences by application to space-time are obvious, and may be of interest by leading directly to a description of the electromagnetic field.
Book
Differential Geometry of Spray and Finsler Spaces
TL;DR: In this paper, the authors introduce the concept of Finsler Spaces of Scalar Curvature, which are derived from Minkowski Spaces and Structure Equations of Sprays.
Book
The theory of sprays and Finsler spaces with applications in physics and biology
TL;DR: In this article, the authors introduce the concept of Connections in Finsler Spaces and introduce the notion of FINslerian physics. But they do not discuss the relationship between the two concepts.