Metrics Of Eguchi-Hanson Types And Its Properties

This thesis mainly studies the Eguchi-Hanson type metrics and its properties by using the knowledge of differential geometry.And in this paper,we constructed two types of Eguchi-Hanson metric with negative constant scalar curvature.For the Eguchi-Hanson type I metric,it has the K(?)hler structure,but it is not asymptotically hyperbolic.The Eguchi-Hanson type? metric is asymptotically hyperbolic,and its total energy may be negative.