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A principal circle bundle over a real hypersurface of a complex projective space CPⁿ can be regarded as a hypersurface of an odd-dimensional sphere. From this standpoint we can establish a method to translate conditions imposed on a hypersurface of CPⁿ into those imposed on a hypersurface of S^{2n + 1}. Some fundamental relations between the second fundamental tensor of a hypersurface of CPⁿ and that of a hypersurface of S^{2n + 1} are given.
Mitsutaka Okumura (Wed,) studied this question.
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