  We give asymptotically tight estimates of tangent space variation on
Riemannian submanifolds of Euclidean space with respect to the local feature
size of the submanifolds. We show that the result follows directly from
structural properties of local feature size of the Riemannian submanifold and
some elementary Euclidean geometry. We also show that using the tangent
variation result one can prove a new structural property of local feature size
function. This structural property is a generalization of a result of Giesen
and Wagner [GW04, Lem. 7].
