Identically solvable finsler geometries
2010jdw | Garasko G.I.  // Research Institute of Hypercomplex Systems in Geometry and Physics, Friazino, Russia, gri9z@mail.ru

We suggest an algorithm to search for the identically solvable Finsler geometries which provides the possibility to find some solvable Finsler geometries that are not identically solvable. This algorithm is closely related to the reflection on the space whose dimension is one unit less than the dimension of the Finsler space on itself. This reflection must coincide to its own reverse and possess some other properties. For the spaces of arbitrary dimension, the identical reflection corresponds to the Euclidean space, the reflection with the simultaneous change of the sign of all coordinates - to the pseudo Euclidean space, and the reflection with the inversion of all the coordinates corresponds to the space with Berwald-Moor metric.

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