1 CONSTRUCTIONS IN SASAKIAN GEOMETRY

A Riemannian manifold (M, g) is called a Sasakian manifold if there exists a Killing vector field ξ of unit length on M so that the tensor field Φ of type (1, 1), defined by Φ(X) = −∇Xξ, satisfies the condition (∇XΦ)(Y) = g(X, Y)ξ − g(ξ, Y)X fo any pair of vector fields X and Y on M. This is a curvature condition which can be easily expressed in terms the Riemann curvatur