On g-natural metrics with constant scalar curvature on unit tangent sphere bundle

Abstract

Over a Riemannian manifold (M,g),we study the geometry of all natural metrics of classical type induced on the unit tangent sphere bundle. In the 3-dimensional case, we derive necessary and sufficient conditions for such metrics to have constant scalar curvature.

Keywords

• g-natural
• metrics
• constant
• scalar
• curvature
• tangent
• sphere
• bundle