A NOTE ON GENERALIZED LICHNEROWICZ-OBATA THEOREMS FOR RIEMANNIAN FOLIATIONS

Pak, Hong-Kyung; Park, Jeong-Hyeong

doi:10.4134/BKMS.2011.48.4.769

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A NOTE ON GENERALIZED LICHNEROWICZ-OBATA THEOREMS FOR RIEMANNIAN FOLIATIONS

Journal title : Bulletin of the Korean Mathematical Society
Volume 48, Issue 4, 2011, pp.769-777
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2011.48.4.769

Title & Authors

A NOTE ON GENERALIZED LICHNEROWICZ-OBATA THEOREMS FOR RIEMANNIAN FOLIATIONS
Pak, Hong-Kyung; Park, Jeong-Hyeong;

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;

Language

English

Cited by

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