We characterize totally η-umbilic real hypersurfaces in a nonflat complex space form [...](c) (= CPn(c) or CHn(c)) and a real hypersurface of type (A2) of radius π/(2√c) in CPn(c) by observing the shape of some geodesies on those real hypersurfaces as curves in the ambient manifolds (Theorems 1 and 2).
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