Basic Dolbeault cohomology and Weitzenb\"ock frmulas on transversely K\"ahler foliations
Seoung Dal Jung, Ken Richardson
TL;DR
This paper explores basic Dolbeault cohomology and derives new Weitzenb"ock formulas for transversely K"ahler foliations, revealing how curvature conditions influence harmonic forms.
Contribution
It introduces new Weitzenb"ock formulas and analyzes curvature conditions that restrict basic Dolbeault cohomology on transversely K"ahler foliations.
Findings
Positive transversal Ricci curvature implies no nonzero basic-harmonic forms of type (r,0)
Derived new Weitzenb"ock formulas for transversely K"ahler foliations
Identified curvature conditions affecting basic Dolbeault cohomology
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 , among other results.
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