Talk by Professor Gideon Maschler, Clark University

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Venue:DM 409A

Tuesday, January 12, 3:30-4:30pm, DM 409A, Professor Gideon Maschler, Clarks University,

Title: Distinguished metrics in conformal classes

Abstract: The appearance of two Riemannian metrics in a conformal class on a given manifold, both satisfying a curvature restriction, is typically an overdetermined problem that often allows classification. Various cases have been studied at least since the 1920's. More recently examined is the case where only one of the metrics is curvature-distinguished, while the other is Kahler. We first briefly describe the case where the first of the two metrics is Einstein, where a fairly complete description can be given, even globally. We then turn to other first metric types, such as a gradient Ricci soliton, and, if time permits, versions of the Einstein and soliton conditions that are adapted to warped product constructions. In these latter cases much more limited results are known, but we are still able to give a partial local classification and some rigidity results in special cases.