Nonexistence of Levi-degenerate hypersurfaces of constant signature in CPn

摘要

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