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Basic Dolbeault cohomology and Weitzenböck frmulas on transversely Kähler foliations (1709.05469v1)
Published 16 Sep 2017 in math.DG
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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