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Transverse conformal Killing forms and a Gallot–Meyer theorem for foliations

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We study transverse conformal Killing forms on foliations and prove a Gallot–Meyer theorem for foliations. Moreover, we show that on a foliation with C-positive normal curvature, if there is a closed basic 1-form \({\phi}\) such that \({\Delta_B\phi=qC\phi}\), then the foliation is transversally isometric to the quotient of a q-sphere.

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Authors and Affiliations

  1. Department of Mathematics and Research Institute for Basic Sciences, Jeju National University, Jeju, 690-756, Korea

    Seoung Dal Jung

  2. Department of Mathematics, Texas Christian University, Fort Worth, TX, 76129, USA

    Ken Richardson

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  1. Seoung Dal Jung
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  2. Ken Richardson
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Correspondence to Seoung Dal Jung.

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Jung, S.D., Richardson, K. Transverse conformal Killing forms and a Gallot–Meyer theorem for foliations. Math. Z. 270, 337–350 (2012). https://doi.org/10.1007/s00209-010-0800-8

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  • DOI: https://doi.org/10.1007/s00209-010-0800-8

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