Perspectives in Riemannian Geometry

The papers in this volume are written by some of the participants of the Short Program in Riemannian Geometry held at the Centre de Recherche Mathématiques, Montreal, 2004. The main topics of the proceedings are covered by three papers based on lectures given by M. Anderson, K. Grove and N. J. Hitchin. The first paper is Anderson’s comprehensive survey of recent results on the existence of Einstein metrics on open manifolds with a certain structure at infinity. The second paper (complementing the topic) is the Biquard survey of Einstein metrics with asymptotic structure at infinity modelled on the complex hyperbolic space and their applications to CR geometry. The Grove lecture notes survey comparison geometry, mainly in the framework of lower bounds of sectional curvatures. Hitchin addresses the question of special geometry in dimensions 6, 7 and 8 and their relation to the geometry of open orbits of Lie groups.

Another two papers in the volume are concerned with special geometric structures. R. Bryant's paper provides a systematic study of a class of special Lagrangian submanifolds in complex domains, and A. Dancer together with M. Wang explain their Hamiltonian approach to cohomogeneity one Einstein metrics. Three of the papers are devoted to the interaction between Riemannian and complex geometry (the paper by C. Boyer and K. Galicki is a survey of new Sasaki-Einstein metrics build out of Kähler-Einstein orbifolds; L. David and P. Gauduchon's paper provides a thorough study of Bochner-flat Kähler orbifolds from the point of view of the CR-geometry of the standard sphere; and C. LeBrun's paper studies the stability of complex curves with boundary in twistor spaces appearing in the new approach to Zoll manifolds). The last paper by A. Nabutovsky contains a survey of the relationship between the space of Riemannian structures on closed manifolds, computability theory and algorithmic information theory.

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