In [2] , S. Bochner defined a certain curvature tensor as a complex analogy of Weyl conformal curvature tensor without geometrical interpretation. At present this tensor is called Bochner curvature tensor. Recently Webster [9], [11] gave this geometrical interpretation as a pseudoconformal invariant on a Ci?-manifold. Indeed Bochner curvature tensor is the 4th curvature invariant given in Chern-Moser's paper [4] (cf. Tanaka [7]). In this paper we shall also derive Bochner curvature tensor from

more »

... ur argument of Ci?-structure. In [6] we studied almost contact structures standing on the viewpoint of pseudoconformal geometry and gave the change of canonical connections associated with almost contact structures belonging to the same Ci?-structure. The point under our discussion is the fact that almost contact structures belonging to a Ci?-structure play the same role as Riemannian structures belonging to a conformal structure and canonical connections correspond to Riemannian connections. Like the conformal change of Riemannian connections, a gradient vector appears in the change of canonical connections. Therefore we compute the difference of their curvature tensors and eliminate the gradient vector. Then we get a curvature invariant. In § 1 we recall definitions and results given in [6] . § 2 is devoted to the study of curvatures of canonical connections. We in § 3 obtain the curvature invariant of the pseudo-conformal geometry. The authors wish to express their hearty thanks to Professor S. Ishihara for his constant encouragement and valuable suggestions. § 1. Preliminaries. Let J be a connected orientable C°°-manifold of dimension 2n+l (n^l) and (£), J) a pair of a hyperdistribution 3) and a complex structure / on £). The pair (3), J) is called a CR-structure if the following two conditions hold: (c.i) zjχ,m-zχ, (C.2) ZJX, JYl-lX, Yl-ΛZX, JYl+ZJX, O=