Universität Augsburg
Institut für Mathematik

The Yamabe problem is a classical problem on how to find Riemannian metrics of constant scalar curvature in a given conformal class. This problem can be written as a PDE, and positive solutions can always be found. On the other hand, the problem of finding general solutions to the Yamabe PDE turns out to be a very complicated one.

A possible approach to solve in general the Yamabe PDE is to assume the presence of "symmetries" to have extra constraints in the equation. Given that group actions by isometries and geometric projections are particular types of singular Riemannian foliations, in this talk we consider singular Riemannian foliations as a form of symmetry. Using this notion of symmetry together with techniques of calculus of variations, we show how to find an infinite number of general solutions to the Yamabe problem, which are constant along the leaves of the foliation.