THE STANDARD CR STRUCTURE ON THE UNIT TANGENT BUNDLE

Dedicated to Professor Takesi Kotake on his sixtieth birthday

Abstract

The unit tangent bundle of a Riemannian manifold is one of popular examples of contact manifolds. It has the standard CR structure which is not integrable in general. We study the recently defined gauge invariant of type (1, 3) of the CR structure and show that the invariant vanishes, if and only if the Riemannian manifold is of constant curvature -1.