Finsler geometry without line elements faced to applications

In this note we want to introduce Finsler geometry for a wider audience. First the basic concept is sketched and several illuminating examples are given. Then we show the approach to a geometrical study of Finsler geometry where Finsler spaces are regarded as point spaces, in contrast to line element bundles. We define the affine deformation of Finsler spaces, and show that the affmely deformed Minkowski spaces are characterized by the existence of linear metrical connections. We prove that if the indicatrices of an affinely deformed Minkowski space are maximally Iʹ-mobile, then the space is Riemannian, while in the case of Iʹ-rigidity the space is Minkowskian.