Application of an integral formula to CR-submanifolds of complex hyperbolic space

Let M̄ be a complex space form of constant holomorphic sectional curvature c and let M be an n-dimensional CR-submanifold of (n− 1) CR-dimension in M̄. ThenM has an almost contact metric structure (F,U ,u,g) (see Section 2) induced from the canonical complex structure of M̄. Hence on an n-dimensional CR-submanifold of (n− 1) CRdimension, we can consider two structures, namely, almost contact structure F and a submanifold structure represented by second fundamental form A. In this point of view, many differential geometers have classified M under the conditions concerning those structures (cf. [3, 5, 8, 9, 10, 11, 12, 14, 15, 16]). In particular, Montiel and Romero [12] have classified real hypersurfacesM of complex hyperbolic space CH which satisfy the commutativity condition (C)