Differential Geometry Working Seminar

Anton Iliashenko, Department of Pure Mathematics, University of Waterloo

"The third Betti number of nearly Kahler 6-manifolds"

On a Riemannian manifold, Weizenbock formulas relate the usual Laplacian and the rough Laplacian along with Riemannian curvature. We consider 6-dimensional nearly Kahler manifolds and look at how the Weizenbock formula for 3-forms simplifies. We will see that a new curvature-type operator shows up which acts on symmetric 2-tensors. Assuming compactness, it will be possible to conclude the vanishing of the 3rd Betti number from a specific bound on this new operator.

MC 5403