We show an analogue of the Lorentzian splitting theorem for weighted Lorentz-Finsler manifolds: If a Berwald spacetime nonnegative Ricci curvature satisfies certain completeness and metrizability conditions includes timelike straight line, then it necessarily admits one-dimensional family isometric translations generated by gradient vector field Busemann function. Moreover, our formulation in t...

The paper introduces the approach to construction of the Lagrangian of the field (fields). This approach is based solely on the metric function of the Finsler space: the Lagrangian is constructed as the unit divided by the volume swept by the unit vector running through all the points of the indicatrix in the tangent space under the assumption of the tangent space being Euclidean. For the space...

Every Finsler metric naturally induces a spray but not so for the converse. The notion sprays of scalar (resp. isotropic) curvature has been known as generalization metrics flag curvature. In this paper, new notion, constant curvature, is introduced and especially it shows that isotropic necessarily even in dimension $$n\ge 3$$ . Further, complete conditions are given constant) to be metrizable...

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 of the hv-curvature of Cartan connection leads to wrong expressions. On the o...

Scoliosis is the abnormal lateral curvature and rotation of the spine. In the past this deformity has been linked with moral depravity, as in the case of Richard III. Treatment for scoliosis began with Hippocrates's use of boards and axial distortion. Today, bracing and surgery are used either to correct the deformity or to prevent further progression. In the past, however, exercise regimens ha...