Special Metrics on Manifolds

Cuny City College, New York NY

Investigators

Abstract

Dr. Santoro proposes to study special metrics on manifolds. This research project splits into four parts:the construction of complete Ricci-flat Kaehler metrics with special asymptotic behavior, the explicit construction of examples of anti-self dual metrics on 4-manifolds, the existence of Yang-Mills energy minimizers for Calabi-Yau manifolds, and the existence of complete, constant mean curvature hypersurfaces in Hyperbolic Space with prescribed behavior at infinity. It is hard to overestimate the role played by Calabi-Yau Spaces and Yang-Mills Theory in Differential Geometry and Physics. Calabi-Yau manifolds, essentially shapes that satisfy the requirement of space for the six "unseen" spatial dimensions of the present model of Universe, are a key object of research in superstring theory. The problems investigated in this project are among the most natural in their context and possess several interesting additional applications in neighboring areas of Mathematics, such as Complex Geometry and Topology.