Journal of the
Korean Mathematical Society JKMS

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tana-ka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\eta,\varphi)$ with the pseudo-parallel structure operator $h(=1/2L_{\xi}\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schur-type theorem, where $L_\xi$ denote the Lie derivative in the characteristic direction $\xi$.

Keywords: contact strongly pseudo-convex CR-manifold, Sasakian space form, contact strongly pseudo-convex CR-space form

MSC numbers: 53D10, 53C15, 53C25