Abstract
In this paper, we study the twisted basic Dolbeault cohomology and transverse hard Lefschetz theorem on a transverse Kähler foliation. And we give some properties for \(\Delta _\kappa \)-harmonic forms and prove the Kodaira–Serre-type duality and Dolbeault isomorphism for the twisted basic Dolbeault cohomology.
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The author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2022R1A2C1003278).
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Jung, S.D. Twisted basic Dolbeault cohomology on transverse Kähler foliations. Ann Glob Anal Geom 62, 285–303 (2022). https://doi.org/10.1007/s10455-022-09851-3
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DOI: https://doi.org/10.1007/s10455-022-09851-3
Keywords
- Riemannian foliation
- Transverse Kähler foliation
- Basic Dolbeault cohomology
- Twisted basic Dolbeault cohomology
- Kodaira–Serre duality
- Hard Lefschetz theorem