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Let X be a Hadamard manifold. By applying the stable Jacobi tensor along horospherical foliations of X, a characterization of the real space form is obtained by means of the second fundamental form of... the horospheres. The complex space form, the quaternionic space form and the other rank-one symmetric spaces of non-compact type are also similarly characterized. Geometrical characterization of horospheres are also given.続きを見る
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