Non-Euclidean method of the generalized geometry construction and its

application to space-time geometry.

 Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences
 101-1 ,Vernadskii Ave., Moscow, 119526, Russia
 email: rylov@ipmnet.ru
 Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm
or mirror Web site: http://gasdyn-ipm.ipmnet.ru/~rylov/yrylov.htm

Updated February 23, 2007

abstract

Non-Euclidean method of the generalized geometry construction is considered. According to this approach any generalized geometry is obtained as a result of deformation of the proper Euclidean geometry. The method may be applied for construction of space-time geometries. Uniform isotropic space-time geometry other, than that of Minkowski, is considered as an example. The problem of the geometrical objects existence and their temporal evolution may be considered in the constructed space-time geometry. Such a statement of the problem is impossible in the framework of the Riemannian space-time geometry. Existence and dynamics of microparticles is considered to be conditioned by existence of corresponding geometrical objects and their temporal evolution in the space-time. Geometrization of the particle mass and its momentum is produced.

There is text of the paper in English (pdf) and in Russian (ps, pdf)