Pseudo-Finsleroid spatial-anisotropic relativistic space

Finsleroid-regular space developed. Berwald case

The Finsleroid--Finsler space becomes regular when the norm $||b||=c$ of the input 1-form $b$ is taken to be an arbitrary positive scalar $c(x) < 1$. By performing required direct evaluations, the respective spray coefficients have been obtained in a simple and transparent form. The adequate continuation into the regular pseudo-Finsleroid domain has been indicated. The Finsleroid-regular Berwald space is found under the assumptions that the Finsleroid charge is a constant and the 1-form $b$ is parallel. Keywords: Finsler metrics, spray coefficients, curvature tensors.

Two-axes pseudo-Finsleroid metrics: general overview and angle-regular solution

The class of the two-axes pseudo-Finslerian metrics which is specified by the condition of the angle-separation in the involved characteristic functions is proposed and studied. The complete Total Set of algebraic and differential equations is derived in all rigor which are necessary and sufficient in order that a pseudo-Finsleroid metric function belong to the class. It proves possible to solve the equations of the set. The angle-regular solution of the Finsleroid-in-pseudo-Finsleroid type is found and described in detail.

Finsleroids Reflect Future-Past Asymmetry of Space-Time

The Finslerian extension of the Euclidean metric is proposed and studied under rigorous conditions that the associated indicatrix is regular and convex. The relativistic pseudo-Euclidean metric is extended, too. The extensions show distinct violation of the $T-$parity, so that the future-past asymmetry of the physical world can stem from the $T-$asymmetry of the Finslerian indicatrix. Indeed the idea should compel much attention of physicists.

锥形伪芬斯勒力学系统

Conic Pseudo-Finslerian Mechanical Systems

该研究构建了锥形伪芬斯勒流形上保守力学系统的几何框架，推广了经典黎曼力学，建立了守恒律、完备性准则及约束力存在唯一性，为各向异性动力学提供统一几何基础。

Anisotropic conformal invariance of lightlike geodesics in pseudo-Finsler manifolds

In this paper, we prove that lightlike geodesics of a pseudo-Finsler manifold and its focal points are preserved up to reparametrization by anisotropic conformal changes, using the Chern connection and the anisotropic calculus and the fact that geodesics are critical points of the energy functional and Jacobi fields, the kernel of its index form. This result has applications to the study of Finsler spacetimes.

圆锥伪-Finsler曲面的特殊各向异性共形变换

Special anisotropic conformal changes of conic pseudo-Finsler surfaces

本文提出了圆锥伪-Finsler曲面的多种特殊各向异性共形变换，研究了$ϕT$-条件及其等价性，并将理论应用于具有Finslerian球对称性的Schwarzschild-de Sitter解。