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Riemannian foliations admitting transversal conformal fields II

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Abstract

Let \((M,g_M,{\mathcal {F}})\) be a closed, oriented Riemannian manifold with a foliation \({\mathcal {F}}\) of codimension \(q\) and a bundle-like metric \(g_M\). Assume that the transversal scalar curvature is non-zero constant. If \(M\) admits a transversal conformal field satisfying some conditions, then \({\mathcal {F}}\) is transversally isometric to a sphere.

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Acknowledgments

The author would like to thank the referee for the valuable suggestions and the comments. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0021005).

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  1. Department of Mathematics, Jeju National University, Jeju, 690-756, Korea

    Seoung Dal Jung

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  1. Seoung Dal Jung
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Correspondence to Seoung Dal Jung.

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Jung, S.D. Riemannian foliations admitting transversal conformal fields II. Geom Dedicata 175, 257–266 (2015). https://doi.org/10.1007/s10711-014-0039-3

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