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A NOTE ON GENERALIZED LICHNEROWICZ-OBATA THEOREMS FOR RIEMANNIAN FOLIATIONS

  • Received : 2009.12.10
  • Published : 2011.07.31

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

References

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