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Geometric meaning of Sasakian space forms from the viewpoint of submanifold theory
We show that M2n-1 is a real hypersurface all of whose geodesics orthogonal to the characteristic vector ξ are mapped to circles of the same curvature 1 in an n-dimensional nonflat complex space form $\widetilde{M}_n$(c) (= CPn(c) or CHn(c)) if and only if M is a Sasakian manifold with respect …