We study properties of the mean curvature one-form and its holomorphic and antiholomorphic cousins on a transverse Kähler foliation. If the mean curvature of the foliation is automorphic, then there are some restrictions on basic cohomology similar to that on Kähler manifolds, such as the requirement that the odd basic Betti numbers must be even. However, the full Hodge diamond structure does not apply to basic Dolbeault cohomology unless the foliation is taut.
Cite this article
Seoung Dal Jung, Ken Richardson, The Mean Curvature of Transverse Kähler Foliations. Doc. Math. 24 (2019), pp. 995–1031DOI 10.4171/DM/698