Nonexistence of Levi-degenerate hypersurfaces of constant signature in CPn

Abstract

Let M be a smooth hypersurface of constant signature in CPⁿ, n≥3. We prove the regularity for $\bar{∂}_b$ on M in bidegree (0,1). As a consequence, we show that there exists no smooth hypersurface in CPⁿ, n≥3, whose Levi form has at least two zero-eigenvalues.