Curvatures of weighted metrics on tangent sphere bundles
Received: 29 April 2011
Accepted in revised form: 6 September 2011
Mathematics Subject Classification (2010): 53A30, 53C17, 53C21.
Keywords: Metric connection, tangent sphere bundle, curvature.
Abstract: We determine the curvature equations of natural metrics on tangent bundles and radius r tangent sphere bundles Sr M of a Riemannian manifold M. A family of positive scalar curvature metrics on Sr M is found, for any M with bounded sectional curvature and any chosen constant r.