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In this paper, for any compact Lie group G G , we show that the space of G G -equivariant Riemannian metrics with positive scalar curvature (PSC) on any closed three-manifold is either empty or contractible. In particular, we prove the generalized Smale conjecture for spherical three-orbifolds. Moreover, for connected G G , we make a classification of all PSC G G -equivariant three-manifolds.
Chow et al. (Thu,) studied this question.