Envelopes of legendre curves in the unit spherical bundle over the unit sphere

In this paper, we introduce a one-parameter family of Legendre curves in the unit spherical bundle over the unit sphere and the curvature. We give the existence and uniqueness theorems for one-parameter families of spherical Legendre curves by using the curvatures. Then we define an envelope for the one-parameter family of Legendre curves in the unit spherical bundle. We also consider the parallel curves and evolutes of one-parameter families of Legendre curves in the unit spherical bundle and their envelopes. Moreover, we give relationships among one-parameter families of Legendre curves in the unit spherical bundle over the unit sphere and one-parameter families of Legendre curves in the unit tangent bundle over the Euclidean plane.