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On Levi flat hypersurfaces with transversely affine foliation

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We prove the non-existence of real analytic Levi flat hypersurface whose complement is 1-convex and Levi foliation is transversely affine in a compact Kähler surface.

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Acknowledgements

We thank Carolina Canales González for explaining some details of her work [4]. We are grateful to Yoshihiko Mitsumatsu and Noboru Ogawa for pointing out inaccuracies in the first draft of this paper, and to the referees for their thorough remarks.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka, 422-8529, Japan

    Masanori Adachi

  2. Université Polytechnique Hauts-de-France, Ceramaths, FR CNRS 2956, 59313, Valenciennes, France

    Séverine Biard

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  1. Masanori Adachi
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  2. Séverine Biard
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Correspondence to Séverine Biard.

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We acknowledge the support from Watanabe Trust Fund of the University of Iceland. Masanori Adachi is partially supported by a JSPS KAKENHI Grant Number JP18K13422.

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Adachi, M., Biard, S. On Levi flat hypersurfaces with transversely affine foliation. Math. Z. 301, 373–383 (2022). https://doi.org/10.1007/s00209-021-02927-z

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  • DOI: https://doi.org/10.1007/s00209-021-02927-z

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