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Let Pn(C) denote an ^-dimensional complex projective space with the FubiniStudy metric of constant holomorphic sectional curvature Ac and M a real hypersurface in Pn{C) with the induced metric. The problem with respect to the type number t,i.e.,the rank of the second fundamental form of real hypersurfaces in Pn{C) has been studied by many differentialgeometers ([1],[2] and [3] etc.). The second named author [4] showed that there is a point p on M such that t{p) > 2 and M. Kimura and S. Maeda [1] gave an example of real hypersurface in Pn{C) satisfying t ― 2, which is non-complete. Y. J. Suh [3] proved that there is a point p on a complete real hypersurface M in Pn(C) (≪> 3) such that t(p) > 3. According to [2],there is a point p on a complete real hypersurface M in Pn(C) such that t(p) > n, but thereis a mistake in deducation to lead a certain formula. In this paper, we shall prove the following Main theorem

A note on the type number of real hypersurfaces in $P_{n}(C)$