We propose a new framework for constructing geometric and physical models on nonholonomic manifolds provided both with Clifford – Lie algebroid symmetry and nonlinear connection structure. Explicit parametrizations of generic off–diagonal metrics and linear and nonlinear connections define different types of Finsler, Lagrange and/or Riemann–Cartan spaces. A generalization to spinor fields and D...

In this paper, by the Gauss equation of the induced Chern connection for Finsler submanifolds, we prove that if M is an umbilical hypersurface of a Minkowski space (V , F ), then either M is a Riemannian space form or a locally Minkowski space. AMS subject classifications: 53C60, 53C40

Kinematics in Finsler space is used to study the propagation of ultra high energy cosmic rays particles through the cosmic microwave background radiation. We find that the GZK threshold is lifted dramatically in Randers-Finsler space. A tiny deformation of spacetime from Minkowskian to Finslerian allows more ultra-high energy cosmic rays particles arrive at the earth. It is suggested that the l...

In this paper, we obtain a Nakano type inequality for vertical valued ∂h harmonic mixed forms with compact support on the total space of the holomorphic tangent bundle of a complex Finsler manifold. AMS subject classifications: 53B40, 32L20

This paper introduces a novel steepest descent flow in Banach spaces. This extends previous works on generalized gradient descent, notably the work of Charpiat et al. [12], to the setting of Finsler metrics. Such a generalized gradient allows one to take into account a prior on deformations (e.g., piecewise rigid) in order to favor some specific evolutions. We define a Finsler gradient descent ...