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Let ( M ,  g ) be a compact manifold with boundary and $$Ric_g\ge (n-1)g$$ R i c g ≥ ( n - 1 ) g , Hang and Wang proved that ( M ,  g ) is isometric to the standard hemisphere if $$\partial M$$ ∂ M is convex and isometric to $${\mathbb {S}}^{n-1}(1)$$ S n - 1 ( 1 ) . We prove some rigidity theorems when $$\partial M $$ ∂ M is isometric to a product manifold where one factor is the standard sphere.

A note on Hang-Wang’s hemisphere rigidity theorem