Vadim Knizhnik [obituary]
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.
We consider the cohomoly groups of compact locally Hermitian symmetric spaces with coefficients in the sheaf of germs of holomorphic sections of those vector bundles over the spaces which are defined by canonical automorphic factors. We give a quick survey of the research on these cohomology groups, and then discuss vanishing theorems of the cohomology groups.
Le but de cet article est d’exposer de nouveaux exemples de structures anti-de Sitter sur des fibrés en cercles au-dessus d’une surface hyperbolique qui ne sont pas, modulo revêtement et quotient finis, des déformations de structures homogènes.
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.
Three results are shown which demonstrate how Vassiliev invariants behave like polynomials.
This paper determines the possible Stiefel-Whitney classes for vector bundles over Dold manifolds.