Riemannian Geometry

We consider the “inner” geometry of a manifold which is not a part of an euclidean space. We consider only tangential vectors, and any vector normal to the manifold is not available. We presuppose that each tangent bundle possesses an inner product depending on points of its base space smoothly. The space is curved in general. The Riemannian curvature of a manifold governs the behavior of geodesics on it and corresponding dynamical system. Dimension of the manifold is not always finite.