Strongly pseudo-convex CR space forms

Abstract

For a contact manifold, we study a strongly pseudo-convex CR space form with constant holomorphic sectional curvature for the Tanaka-Webster connection. We prove that a strongly pseudo-convex CR space form M is weakly locally pseudo-Hermitian symmetric if and only if (i) dim M = 3, (ii) M is a Sasakian space form, or (iii) M is locally isometric to the unit tangent sphere bundle T1(𝔿n+1) of a hyperbolic space 𝔿n+1 of constant curvature −1.

Keywords

• contact manifold
• strongly pseudo-convex cr space form
• pseudo-hermitian symmetry
• 53c15
• 53c25
• 53d10