Quasijets in anisotropic media, Finsler geometry, and Fermi coordinates

The Hamilton-Jacobi equations for the phase function of quasijet solutions in the case of Finsler geometry are considered. This case corresponds to the physical problem of wave propagation in anisotropic media. The wave field corresponding to a quasijet solution propagates along a geodesic. For this reason, all computations are performed in Fermi coordinates near a geodesic. Upon extracting the frequency factor, the quadratic term of the phase function satisfies the covariant Riccati equation. A notably simple form for the equation is obtained in the case of Riemannian geometry. The nontrivial coefficients of the Riccati equation coincide with the elements of the curvature tensor. In the case of Finsler geometry, all considerations are more complicated. Nevertheless, of cricial importance in the Riccati equation are the elements of the third Cartan curvature tensor computed at tangential elements to the geodesic. Bibliography: 10 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 332, 2006, pp. 48–69.