A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Researchers generalize cosmological models using Finsler geometry.
As a natural application of the {\it theory of geometric averaging} in Finsler geometry and generalized Finsler geometry, a new approach to investigate {\it generalized Finsler geometry}, based on a convex invariance of the average structures, is introduced.
PhD dissertation on Finsler geometry and gravity, focusing on Berwald spaces and exact solutions.
New approach connects Finsler geometry's metric and connections.
A new connection in Finsler geometry unifies various types of connections.
This paper reviews Douglas curvature in Finsler geometry.
The geometry and analysis on Finsler manifolds is a very important part of Finsler geometry. In this article, we introduce some important and fundamental topics in global Finsler geometry and discuss the related properties and the relationships in them. In particular, we optimize and improve the various definitions of …
Paper studies curvature in Finsler geometry, proving curvature constancy under isotropy.
The paper studies new curvature properties in Finsler geometry.
Paper solves open problem in complex Finsler geometry.
Recover simple irreversible Finsler geometry from travel time data
Here, a non-linear analysis method is applied rather than classical one to study projective Finsler geometry. More intuitively, by means of an inequality on Ricci-Finsler curvature, a projectively invariant pseudo-distance is introduced and an analogous of Schwarz' lemma in Finsler geometry is proved. Next, the Schwarz…
Paper proves inequality linking capillary surfaces to Finsler geometry.
A method to generalize results from Riemannian Geometry to Finsler geometry is presented. We use the method to generalize several results that involve only metric conditions. Between them we show that the topology induced by the Finsler structure is equivalent to the manifold topology, we provide a new proof of the Hop…
Bipartite Riemann-Finsler geometries with complementary Finsler structures are constructed. Calculable examples are presented based on a bilinear-form coefficient for explicit Lorentz violation.
Berwald geometries are Finsler geometries close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which a given Finsler Lagrangian has to satisfy to be of Berwald type. Applied to -Finsler spaces, respectively -Finsler…
Unified geometry for relativity and beyond.
In this paper, we generalize the classification of geodesic orbit spheres from Riemannian geometry to Finsler geometry. Then we further prove if a geodesic orbit Finsler sphere has constant flag curvature, it must be Randers. It provides an alternative proof for the classification of invariant Finsler metrics with $K\e…
Describes links between Finsler and Lorentz geometries for Riemannian geometers.
Study investigates Hashiguchi connection's uniqueness and existence in Finsler geometry.
Effective field theories with explicit Lorentz violation are intimately linked to Riemann-Finsler geometry. The quadratic single-fermion restriction of the Standard-Model Extension provides a rich source of pseudo-Riemann-Finsler spacetimes and Riemann-Finsler spaces. An example is presented that is constructed from a …
Researchers found explicit solutions to a complex equation in advanced geometry.
Lorentz-Finsler geometry reveals new and old inequalities.
Investigates hypersurfaces in Finsler spaces with generalized square metrics.
The aim of the present paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism space (GAP-space). The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space, which we refer to as a Finslerized Pa…
The tangent space is constructed in sub-Finsler geometry, leading to the failure of the CD condition in 3D-contact manifolds.
Finsler geometry connects to higher-spin fields and curved-space Fronsdal equations.
New definition of metric current yields Finsler geometry volume densities.
The correspondence between Riemann-Finsler geometries and effective field theories with spin-independent Lorentz violation is explored. We obtain the general quadratic action for effective scalar field theories in any spacetime dimension with Lorentz-violating operators of arbitrary mass dimension. Classical relativist…
By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive constant sectional curvature, not necessarily of Randers type nor projectively flat, …
Researchers find conditions for autoparallels to be Finsler geodesics.
The book "Handbook of Finsler geometry" has been included with a CD containing an elegant Maple package, FINSLER, for calculations in Finsler geometry. Using this package, an example concerning a Finsler generalization of Einstein's vacuum field equations was treated. In this example, the calculation of the components …
Studying various functionals and associated gradient ows are known problems in differential geometry. The perpose of this article is to provide a general overview of curvature functionals in Finsler geometry and use their information for introducing different gradient ows on Finsler manifolds.
Here, by extending the definition of circle to Finsler geometry, we show that, every circle-preserving local diffeomorphism is conformal. This result implies that in Finsler geometry, the definition of concircular change of metrics, a priori, does not require the conformal assumption.
The pullback approach to global Finsler geometry is adopted. Three classes of recurrence in Finsler geometry are introduced and investigated: simple recurrence, Ricci recurrence and concircular recurrence. Each of these classes consists of four types of recurrence. The interrelationships between the different types of …
New TDA approach using Finsler metrics.
Derives equations of motion for systems with angular momentum on Finsler geometries.
Fundamental solutions found for PDEs in Finsler geometry.
The paper generalizes cyclic metrics in homogeneous Finsler geometry.
The physics of classical particles in a Lorentz-breaking spacetime has numerous features resembling the properties of Finsler geometry. In particular, the Lagrange function plays a role similar to that of a Finsler structure function. A summary is presented of recent results, including new calculable Finsler structures…
A new model uses Lorentz-Finsler geometry to predict wave propagation.
Classifies cosmological Finsler spacetimes, finding viable non-stationary models.
Navigation in Lorentz Finsler geometry induces isoparametric hypersurfaces.
The study extends Obata's theorem and classifies Finsler manifolds with transnormal functions.
The aim of the present paper is to investigate intrinsically the notion of a concircular -vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the concept of a concurrent vector field in Finsler geometry. Some properties of concircular -vector fie…
In Finsler geometry, we use calculus to study the geometry of regular inner metric spaces. In this note I will briefly discuss various curvatures and their geometric meanings from the metric geometry point of view, without going into the forest of tensors.
The paper explores families of Finsler metrics and their properties.
Study on cut locus of submanifolds in Finsler geometry.