Bull. Korean Math. Soc. 2011; 48(4): 769-777
Printed July 1, 2011
https://doi.org/10.4134/BKMS.2011.48.4.769
Copyright © The Korean Mathematical Society.
Hong Kyung Pak and Jeong Hyeong Park
Daegu Haany University, Sungkyunkwan University
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
2020; 57(6): 1501-1509
1993; 30(1): 17-23
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd