|Title:||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.|
|Subject Headings:||Nonnegative sectional curvarture|
Sectional curvature of homogeneous metrics
Homogeneous disc bundles
|Appears in Collections:||Lehrstuhl VII: Differentialgeometrie|
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