On transverse Killing fields of metric foliations¶of manifolds with positive curvature

Abstract

In this paper, we extend a result by H. Takagi on the non-existence of mutually commuting and linearly independent Killing vector fields on positively curved Riemannian manifolds. Further, a kind of “Compact Leaf Theorem” is proved for metric foliations of closed manifolds with positive sectional curvature.