Harmonic foliations on a complex projective space

Abstract

In 1970, D. Ferus [6] gave an estimation on the codimension of a totally geodesic foliationon a sphere and a complex projective space, and successively P. Dombrowski [1] improved his results. Moreover, R. Escobales classified Riemannian foliationssatisfying a certain condition on a sphere and a complex projective space in a series of his papers [2], [3], [4], [5]. On the other hand, F. Kamber and Ph. Tondeur [7], [8] studied the index of harmonic foliations with bundle-like metric on a sphere from a view point of harmonic mappings. Recently, H. Nakagawa and R. Takagi [11] showed that any harmonic foliations on a compact Riemannian manifold of non-negative constant sectional curvature is totally geodesic if the normal plane fieldis minimal. In this paper we will prove