A note on generalized Lichnerowicz-Obata theorems for Riemannian foliations
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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 λ-automorphism with λ= 1- 2/q in the sense of [8]. In the present paper, we extend certain results established in [3] and study Riemannian foliations admitting λ-automorphisms with λ≥ 1- 2/q.
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 λ-automorphism with λ= 1- 2/q in the sense of [8]. In the present paper, we extend certain results established in [3] and study Riemannian foliations admitting λ-automorphisms with λ≥ 1- 2/q.
참고문헌 (12)
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