Differential Geometry of the Lee Models

Abstract

In this dissertation, we study the differential geometry of the Lee Model. The primary result is the differential geometric characterization of the Lee Model. We first construct a special hermitian metric on the Lee model which is invariant under the action of J-biholomorphisms. And we show that the invariant metric actually coincides with the Kobayshi-Royden infinitesimal metric, thus demonstrating an uncommon phenomenon that the Kobayashi-Royden metric is J-hermitian in this case. Then we follow Cartan’s differential-form-approach and find differentialgeometric invariants, including torsion invariants, of the Lee model equipped with this J-hermitian Kobayashi-Royden metric. We also present a theorem that characterizes the Lee model by those invariants, up to J-holomorphic isometric equivalence. In the last part, We present an optimal analysis of the asymptotic behavior of the Kobayashi metric near the strongly pseudoconvex boundary points of domains in almost complex manifolds

our analysis works for all dimensions.