  In this note we introduce the concept of reflective projective varieties.
These are stratified projective varieties with certain dimension constraints on
their dual varieties. We prove that for such varieties, the
Chern-Schwartz-MacPherson classes of the strata completely determine the local
Euler obstructions and the polar degrees. We also propose an algorithm to
compute the local Euler obstructions when such varieties are formed by group
orbits. As examples we compute the local Euler obstructions of quadratic
hypersurfaces and ordinary determinantal varieties to illustrate our method.
