Bulletin of the
Korean Mathematical Society BKMS

It was obtained in [5] generalized Lichnerowicz and Obata theorems for Riemannian foliations, which reduce to the results on Riemannian manifolds for the point foliations. Recently in [3], they studied a generalized Obata theorem for Riemannian foliations admitting transversal conformal fields. Each transversal conformal field is a $\lambda$-automorphism with $\lambda = 1- \frac 2q$ in the sense of [8]. In the present paper, we extend certain results established in [3] and study Riemannian foliations admitting $\lambda$-automorphisms with $\lambda \ge 1- \frac 2q$.

Keywords: Riemannian foliation, generalized Lichnerowicz-Obata theorem, $\lambda$-automorphism, transversally Einstein foliation

MSC numbers: Primary 53C20; Secondary 57R30