  Rare-earth platinum bismuth (RPtBi) has been recently proposed to be a
potential topological insulator. In this paper we present measurements of the
metallic surface electronic structure in three members of this family, using
angle resolved photoemission spectroscopy (ARPES). Our data shows clear
spin-orbit splitting of the surface bands and the Kramers' degeneracy of spins
at the Gamma and M points, which is nicely reproduced with our full-potential
augmented plane wave calculation for a surface electronic state. No direct
indication of topologically non-trivial behavior is detected, except for a weak
Fermi crossing detected in close vicinity to the Gamma point, making the total
number of Fermi crossings odd. In the surface band calculation, however, this
crossing is explained by another Kramers' pair where the two splitting bands
are very close to each other. The classification of this family of materials as
topological insulators remains an open question.
