On the Law of Transformation of Affine Connection and its Integration. Part 1. Generalization of the Lame equations

摘要

The law of transformation of affine connection for n-dimensional manifolds asthe system of nonlinear equations on local coordinates of manifold isconsidered. The extension of the Darboux-Lame system of equations to the spacesof constant negative curvature is demonstrated. Geodesic deviation equation aswell as the equations of geodesics are presented in the form of the matrixDarboux-Lame system of equations.