Osculating spaces and higher order curvature tensors of submanifolds in Rme

This paper is a continuation of the papers [2, 3, 4, 5] and the results are obtained using the recent paper [1]. In this paper are considered the osculating spaces of a submanifold in R-m of the first, second and higher order. Principal curvatures and directions of higher order are also studied, together with their geometrical interpretations. This construction naturally yields to the higher order curvature tensors of submanifolds of the Euclidean spaces.