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• W2254170301 abstract "Let EF be a foliation on a Riemannian manifold M. The distribution on M which is defined to be orthogonal to SF is said to be normal to £Fand denoted by 3L. Nakagawa and Takagi [8] showed that any harmonic foliation on a compact Riemannian manifold of non-negative constant sectional curvature is totally geodesic if the normal distribution is minnimal. And succesively the present author [2] proved a complex version of their result, that is, the above result holds also on a complex projective space with a Fubini-Study metric. However, recently, Li [4] pointed out a serious mistake in the proof of the result of Nakagawa and Takagi, and so of the author's. Therefore those results are now open yet. On the other hand, Li [4] have studied a harmonic foliationon the sphere along the method of Nakagawa and Takagi, and obtained some interesting results. The purpose of this paper is to give a complex analogue of the Li's results. Let Pn+p(C) be the complex projective space with the Fubini-Study metric of constant holomorphic sectional curvature c. Let £Fbe a complex foliation on Pn+p(C) with ^-complex codimention and h the second fundamental tensor of <7. Then we shall Drove the following:" @default.
• W2254170301 created "2016-06-24" @default.
• W2254170301 creator A5062041840 @default.
• W2254170301 date "1992-06-01" @default.
• W2254170301 modified "2023-10-17" @default.
• W2254170301 title "A remark on foliations on a complex projective space with complex leaves" @default.
• W2254170301 cites W1906491520 @default.
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• W2254170301 doi "https://doi.org/10.21099/tkbjm/1496161837" @default.
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