A NOTE ON GENERALIZED LICHNEROWICZ-OBATA THEOREMS FOR RIEMANNIAN FOLIATIONS

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 $\small{{\lambda}}$-automorphism with $\small{{\lambda}=1-{\frac{2}{q}}}$ in the sense of [8]. In the present paper, we extend certain results established in [3] and study Riemannian foliations admitting $\small{{\lambda}}$-automorphisms with $\small{{\lambda}{\geq}1-{\frac{2}{q}}}$.
Keywords
Riemannian foliation;generalized Lichnerowicz-Obata theorem;$\small{{\lambda}}$-automorphism;transversally Einstein foliation;
Language
English
Cited by
1.
A NOTE ON THE GENERALIZED OBATA THEOREM FOR RIEMANNIAN FOLIATIONS,;

Advanced Studies in Contemporary Mathematics, 2012. vol.22. 3, pp.459-465
1.
The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds, Nonlinear Analysis, 2015, 126, 262
2.
A Lower Bound on the Spectrum of the Sublaplacian, The Journal of Geometric Analysis, 2015, 25, 3, 1492
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