On the CR structure of the tangent sphere bundle

Abstract

We adopt the methods of pseudohermitian geometry (cf. [16]) to study the tangent sphere bundle U(M) over a Riemannian manifold M. If M is an elliptic space form of sectional curvature 1 then U(M) is shown to be globally pseudo-Einstein (in the sense of J. M. Lee, [12]).

Keywords

• Tangent sphere bundle
• Webster connection
• Pseudohermitian torsion
• Nonlinear connection
• Sasaki matric