Construction of nonnegatively curved invariant metrics on homogeneous disc bundles

Abstract

In this thesis we analyze under which conditions posed on the boundary metric we can construct nonnegatively curved invariant metrics on homogeneous disc bundles. The metrics we consider are constructed with a method which goes back to Cheeger. In course of analyzing the above stated problem it is shown that an arbitrary invariant metric on a sphere with positive sectional curvature can be extended to a positively curved metric on the ball having the sphere as its boundary, in such a way that the metric is a warped product metric near the boundary. Moreover we analyze in detail under which conditions an invariant metric on the product of an interval and a homogeneous space admits a reparametrization such that the reparametrized metric has nonnegative resp. positive sectional curvature.