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http://dx.doi.org/10.4134/BKMS.2011.48.4.769

A NOTE ON GENERALIZED LICHNEROWICZ-OBATA THEOREMS FOR RIEMANNIAN FOLIATIONS  

Pak, Hong-Kyung (Department of Mathematics Daegu Haany University)
Park, Jeong-Hyeong (Department of Mathematics Sungkyunkwan University)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.4, 2011 , pp. 769-777 More about this Journal
Abstract
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 ${\lambda}=1-{\frac{2}{q}}$ in the sense of [8]. In the present paper, we extend certain results established in [3] and study Riemannian foliations admitting ${\lambda}$-automorphisms with ${\lambda}{\geq}1-{\frac{2}{q}}$.
Keywords
Riemannian foliation; generalized Lichnerowicz-Obata theorem; ${\lambda}$-automorphism; transversally Einstein foliation;
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