To Geometric Aspects of Infinite-Dimensional Dynamical Systems

The main goal of the work is to construct analogues of Christoffel symbols for infinite-dimensional systems and on this basis to obtain geodesic equations for such systems. These analogies are of particular interest in terms of identifying the relationship between the dynamics of systems with an infinite number of degrees of freedom and Riemannian geometry, as well as geometry defined by the pseudo-Riemannian metric.