Finsler manifold - Wikipedia
In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold M where a (possibly asymmetric) Minkowski norm F(x, −) is provided on each tangent space TxM, that enables one to define the length of any smooth curve γ : [a, b] → M as.
Beyond Einstein: Exploring Spacetime Through Finsler Geometry
Jun 27, 2024 · Sjors Heefer’s PhD research explores gravitational waves and spacetime using Finsler geometry, aiming to reconcile general relativity with quantum mechanics. His findings support the Finslerian nature of spacetime, aligning with gravitational wave observations.
An brief introduction to Finsler geometry. Matias Dahl. July 12, 2006. Abstract. This work contains a short introduction to Finsler geometry. Special em-phasis is put on the Legendre transformation that connects Finsler geometry with symplectic geometry. Contents. Finsler geometry 3.
Finsler geometry is nota generalization of Riemannian geometry. It is better described as Riemannian geometry without the quadratic re-striction (2). A special case in point is the inter-esting paper [11]. They studied the Kobayashi metric of the domain bounded by an ellipsoid in C2, and their calculations showed that the
Finsler geometry - Encyclopedia of Mathematics
Jun 5, 2020 · Finsler geometry. A metric generalization of Riemannian geometry, where the general definition of the length of a vector is not necessarily given in the form of the square root of a quadratic form as in the Riemannian case. Such a generalization was first developed in the paper by P. Finsler [1].
[1903.10185] Finsler spacetime geometry in Physics - arXiv.org
Mar 25, 2019 · I review how a pseudo-Finsler spacetime geometry can be defined such that it provides a precise notion of causal curves, observers and their measurements as well as a gravitational field equation determining the Finslerian spacetime geometry dynamically.
An Introduction to Riemann-Finsler Geometry | SpringerLink
Finsler geometry encompasses a solid repertoire of rigidity and comparison theorems, most of them founded upon a fruitful analogue of the sectional curvature. There is also a bewildering array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations.
On Finsler Geometry and Applications in Mechanics: Review and …
Aug 31, 2015 · Finsler geometry encompasses Riemannian, Euclidean, and Minkowskian geometries as special cases, and thus it affords great generality for describing a number of phenomena in physics. Here, descriptions of finite deformation of continuous media …
Introduction to Finsler Geometry In this chapter, we will give a brief introduction to Finsler geometry. Our goal here is twofold. First, although currently Finsler geometry is developing rapidly, it is not as well known as some standard parts of mathematics that are routinely taught in graduate schools.
Comparison Finsler Geometry - SpringerLink
Divided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems.