JournalsdmVol. 24pp. 995–1031

The Mean Curvature of Transverse Kähler Foliations

  • Seoung Dal Jung

    Department of Mathematics, Jeju National University, Jeju 690-756, Republic of Korea

  • Ken Richardson

    Department of Mathematics, Texas Christian University (TCU), Box 298900, Fort Worth, Texas 76129, USA
The Mean Curvature of Transverse Kähler Foliations cover
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Abstract

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. 995–1031

DOI 10.4171/DM/698