Mini-Workshop in Metric Geometry

24 June 2017
Kollegiengebäude Mathematik (Building 20.30)
Europe/Berlin timezone
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Displaying 5 contributions out of 5
A submetry is a natural generalization of a riemannian submersion, which in turn is a natural generalization of an isometry. We will see how certain properties of riemannian submersions remain valid for submetries provided one is willing to relax their definitions. In particular, the notion of parallel translation along arbitrary paths has a natural generalization. Existence and uniqueness are no ... More
Presented by Prof. Pedro SOLÓRZANO on 24 Jun 2017 at 10:45
In this talk we will see that given a closed, orientable Alexandrov space (X,d) we will define an integral current T defined on X with weight equal to 1 and boundary of T equal to zero. In other words, this extends to Alexandrov Spaces the canonical current defined on a closed oriented Riemannian manifold. We will recall that non collapsing sequences of closed oriented compact Riemannian manifol ... More
Presented by Prof. Raquel PERALES on 24 Jun 2017 at 13:30
Alexandrov spaces constitute a synthetic generalization of Riemannian manifolds with a lower bound on sectional curvature. They provide a natural metric setting to study notions of global Riemannian geometry, and therefore, a fundamental problem is that of extending to Alexandrov spaces what is known for Riemannian manifolds. As in the Riemannian case, one may investigate Alexandrov spaces via the ... More
Presented by Prof. Jesus NÚÑEZ-ZIMBRÓN on 24 Jun 2017 at 14:45
Given a semi-Riemannian manifold $\bar M$ with metric $\bar g$, a submanifold $M$ of $\bar M$ is null if the restriction $g$ of $\bar g$ to $M$ is degenerate. These objects deserve some attention, because of their connection with some areas like the study of black holes and others. In general, some properties of $M$ cannot be studied with the usual differential geometric methods, but here we discu ... More
Presented by Prof. Oscar PALMAS on 24 Jun 2017 at 09:30
Our understanding of $3$--manifolds has illuminated two distinct classes of importance; hyperbolic manifolds and graphmanifolds. These are by now considered the basic blocks featured in the geometrisation program of Thurston, famously consolidated by Perelman. From one perspective graph manifolds are exactly the manifolds that {\it collapse}, in the sense that they admit a family of smooth met ... More
Presented by Prof. Pablo SUÁREZ SERRATO on 24 Jun 2017 at 16:30