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We construct integrable PT-symmetric nonlocal reductions for an integrable hierarchy associated with the special orthogonal Lie algebra      so ⁡  ( 3 , R ) \operatorname {so}(3,\mathbb {R})      . The resulting typical nonlocal integrable equations are integrable PT-symmetric nonlocal reverse-space, reverse-time and reverse-spacetime nonlinear Schrödinger equations associated with      so ⁡  ( 3 , R ) \operatorname {so}(3,\mathbb {R})      .

Integrable nonlocal nonlinear Schrödinger equations associated with 𝑠𝑜(3,ℝ)