Rui Albuquerque

Curvatures of weighted metrics on tangent sphere bundles

Pages: 299-313
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.

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Abstract: We determine the curvature equations of natural metrics on tangent bundles and radius r tangent sphere bundles S_r M of a Riemannian manifold M. A family of positive scalar curvature metrics on S_r M is found, for any M with bounded sectional curvature and any chosen constant r.