Szegő Kernel Asymptotics on Complete Strictly Pseudoconvex CR Manifolds

Abstract

We prove a Bochner–Kodaira–Nakano formula and establish Szegő kernel expansions on complete strictly pseudoconvex CR manifolds with transversal CR $$\mathbb {R}$$ R -action under certain natural geometric conditions. As a consequence we show that such manifolds are locally CR embeddable.