Applications of a fundamental exterior differential system

Por Rui Albuquerque (Universidade de Évora).

Abstract: We present a fundamental exterior differential system associated to any given oriented Riemannian manifold of any given dimension. New equations of Riemannian geometry are found. The differential system coincides with the Cartan structural equations in the 2-dimensional case and had recent developments in 3-dimensions. We show several applications in some particular fields of study, such as weak holonomies, Einstein manifolds and hypersurface theory.

Intersection theory in a nearlysmooth complex space

Por Daniel Barlet (Inst. Élie Cartan, Lorraine).

Abstract: We shall explain how the classical intersection theory of cycles in a complex manifold is generalized to an ambient nearly smooth complex space. A key point is the local moving lemma for cycles in a complex manifold. The new phenomenon is the fact that the intersection multiplicity of two integral cycles may be a rational not integral number in this context.