Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a nondegenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a family...

Berwald geometries are Finsler close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which given Lagrangian has satisfy be of type. Applied $(\alpha,\beta)$-Finsler spaces, respectively $(A,B)$-Finsler spacetimes, this reduces condition for the Levi-Civita covariant derivative defining $1$-form. illustrate...

The Chern–Rund connection from Finsler geometry is settled in the generalized Lagrange spaces. For the geometry of these spaces, we refer to [5]. Mathematics Subject Classification: 53C60

‎In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension five‎. ‎Then we explicitly give the flag curvature formulae and the $S$-curvature formulae for the Randers metrics of Douglas type on these spaces‎. ‎Moreover‎, ‎we prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of D...

We show that the equations of motion governing dynamics strings in a compact internal space can be written as dispersion relations, with local speed depends on velocity and curvature string large dimensions. From $(3+1)$-dimensional perspective these viewed relations for waves propagating interior are analogous to those current-carrying topological defects. This allows us construct unified fram...

In [Mu1] we underlined the motifs of holomorphic subspaces in a complex Finsler space: induced nonlinear connection, coupling connections, and the induced tangent and normal connections. In the present paper we investigate the equations of Gauss, H−and A−Codazzi, and Ricci equations of a holomorphic subspace. We deduce the link between the holomorphic curvatures of the Chern-Finsler connection ...

in this paper, we study a special class of generalized douglas-weyl metrics whose douglas curvature is constant along any finslerian geodesic. we prove that for every landsberg metric in this class of finsler metrics, ? = 0 if and only if h = 0. then we show that every finsler metric of non-zero isotropic flag curvature in this class of metrics is a riemannian if and only if ? = 0.

Gravitational field equations in Randers-Finsler space of approximate Berwald type are investigated. A modified Friedmann model is proposed. It is showed that the accelerated expanding universe is guaranteed by a constrained RandersFinsler structure without invoking dark energy. The geodesic in Randers-Finsler space is studied. The additional term in the geodesic equation acts as repulsive forc...

We extend the classical Crofton formulas in Euclidean integral geometry to Finsler metrics on Rn whose geodesics are straight lines.

Nielsen [3] recently asked the following question: ”What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation U , without the use of ancilla qubits?” Nielsen was able to prove that a lower bound on the minimal size circuit is provided by the length of the geodesic between the identity I and U , where the length is defined by a suitable Finsler ...