Curvatures of weighted metrics on tangent sphere bundles

Abstract

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

Cited by in corpus (4)

• Homotheties and topology of tangent sphere bundles
• Notes on the Sasaki metric
• A fundamental differential system of Riemannian geometry
• A fundamental differential system of 3-dimensional Riemannian geometry