27 citations · 166 across the 27 of their papers we have counts for
27 papers
Laplace and Dolbeault operators on Sasakian manifolds
Georges Habib, Ken Richardson, Robert Wolak
Sasakian manifolds, the odd-dimensional analogues of Kähler manifolds, carry two natural pairs of first-order Dolbeault-type operators on the full complex of differential forms, ex…
Transverse geometric formality
Georges Habib, Ken Richardson, Robert Wolak
A Riemannian metric on a closed manifold is said to be geometrically formal if the wedge product of any two harmonic forms is harmonic; equivalently, the interior product of any tw…
Some remarks on equivariant elliptic operators and their invariants
Jochen Brüning, Ken Richardson
In this expository article, we consider first order elliptic differential operators acting on smooth vector bundles over compact manifolds, and certain invariants derived from the…
New cohomological invariants of foliations
Georges Habib, Ken Richardson
Given a smooth foliation on a closed manifold, basic forms are differential forms that can be expressed locally in terms of the transverse variables. The space of basic forms yield…
The mean curvature of transverse Kähler foliations
Seoung Dal Jung, Ken Richardson
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 autom…
Basic Dolbeault cohomology and Weitzenböck frmulas on transversely Kähler foliations
Seoung Dal Jung, Ken Richardson
We study basic Dolbeault cohomology and find new Weitzenböck formulas on a transversely Kähler foliation. We investigate conditions on mean curvature and Ricci curvature that impos…