Unicity of the Lie product
We establish in this paper a lower bound for the volume of a unit vector field defined on , . This lower bound is related to the sum of the absolute values of the indices of at and .
A manifold is said to be Hessian if it admits a flat affine connection and a Riemannian metric such that where is a local function. We study cohomology for Hessian manifolds, and prove a duality theorem and vanishing theorems.
The paper is an overview of our results concerning the existence of various structures, especially complex and quaternionic, in 8-dimensional vector bundles over closed connected smooth 8-manifolds.
This paper determines the possible Stiefel-Whitney classes for vector bundles over Dold manifolds.