GENERALIZED GOTTLIEB AND WHITEHEAD CENTER GROUPS OF SPACE FORMS.

We extend Oprea's result that the Gottlieb group G₁(핊²ⁿ⁺¹/H) is ZH (the center of H) and show that for a map f : A → 핊²ⁿ⁺¹/H, under some conditions on A, we have ^Gf₁ (핊²ⁿ⁺¹/H) =ZHf*(π1(A)), the centralizer of the image f*(π1(A)) in H. Then, we compute or estimate the groups Gf m(핊²ⁿ⁺¹/H) and P^f_m (핊²ⁿ⁺¹/H) for certain m > 1. [ABSTRACT FROM AUTHOR]