Journal ArticleDOI
Projectively flat Randers metrics with constant flag curvature
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In this paper, the authors classify locally projectively flat Randers metrics with constant Ricci curvature and obtain a new family of Randers metric with negative constant flag curvature.Abstract:
We classify locally projectively flat Randers metrics with constant Ricci curvature and obtain a new family of Randers metrics of negative constant flag curvature.read more
Citations
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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
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.
Posted Content
On the Flag Curvature of Finsler Metrics of Scalar Curvature
TL;DR: In this paper, the flag curvature of a Finsler metric is defined as a scalar function on the slit tangent bundle, and the curvature is determined when certain non-Riemannian quantities such as Cartan torsion and Landsberg curvature are isotropic.
Journal ArticleDOI
Randers metrics with special curvature properties
Xinyue Chen,Zhongmin Shen +1 more
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On the Flag Curvature of Finsler Metrics of Scalar Curvature
TL;DR: In this article, the flag curvature of a Finsler metric with isotropic S-curvature is studied and the curvature is partially determined when certain non-Riemannian quantities such as Cartan torsion, Landsberg curvature and S-Curvature vanish.
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.