Symmetry preserving solutions to the Yamabe Problem

Abstract: The Yamabe problem ask whether we can find for a given smoooth Riemannian manifold a representative with constant scalar curvature in the conformal class of the given Riemannian metric. In this talk we consider such a problem under the extra constrain of preserving symmetry. Namely I present that, under mild geometry conditions, we can find solutions to the Yamabe problem which will also respect the symmetry structure given by a singular Riemannian foliation. Singular Riemannian foliations are generalizations of group actions by isometries and fiber bundles.

In other words given a smooth Riemannian manifold with a smooth Riemannian foliation, we can find a conformal representative of the metric, such that it has prescribed scalar curvature and the partition of the manifold by the leafs, is again a singular Rieamnnian foliation.

differential geometry

Audience: researchers in the topic

( paper | video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Riemannian geometry.

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, send a message to geometrywithsymmetries@gmail.com requiring it.

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