On the tangency of degree k of orbits of 1-parameter subgroups (Q789756)

The author characterizes tangent orbits of 1-parameter subgroups of Lie groups using Lie algebraic methods. - A representative result of this paper is the following, where H is a closed subgroup of a Lie group G. ''If the orbit of a 1-parameter subgroup in a reductive homogeneous space \(G/H=M\) is tangent of degree 2 to a geodesic of the canonical connection at the origin 0\(\in M\), then they coincide.''