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arXiv · 1709.05469

Basic Dolbeault cohomology and Weitzenb\"ock frmulas on transversely K\"ahler foliations

Seoung Dal Jung·Ken Richardson
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Abstract

We study basic Dolbeault cohomology and find new Weitzenb\"ock formulas on a transversely K\"ahler foliation. We investigate conditions on mean curvature and Ricci curvature that impose restrictions on basic Dolbeault cohomology. For example, we prove that on a transversely K\"ahler foliation with positive transversal Ricci curvature, there are no nonzero basic-harmonic forms of type $(r,0)$, among other results.

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Seoung Dal Jung, Ken Richardson. 2017-09-16. Basic Dolbeault cohomology and Weitzenb\"ock frmulas on transversely K\"ahler foliations. https://doi.org/10.1142/s1793525320500260

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