Abstract
The Poincaré model of the Lobačevskii geometry is derived from the Fermat principle. The Lobačevskii geometry is interpreted as the Lobačevskii-Fok velocity space geometry of moving particles. The relation of this geometry to the decay of the neutral pi-meson is considered. The generalization of the Lobačevskii geometry is performed and the new angle of parallelism is derived. The light confined circularly in the optical medium is defined as the optical black hole. The existence of the centrifugal force acting on the photon is discussed.
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