We construct normal forms for Levi degenerate hypersurfaces of finite type in C. As one consequence, an explicit solution to the problem of local biholomorphic equivalence is obtained. Another consequence determines the dimension of the stability group of the hypersurface.

We prove that if (M, g) is a compact locally irreducible Riemannian manifold with nonnegative isotropic curvature, then one of the following possibilities hold: (i) M admits a metric with positive isotropic curvature (ii) (M, g) is isometric to a locally symmetric space (iii) (M, g) is Kähler and biholomorphic to CP n. This is implied by the following two results: (i) Let (M, g) be a compact, l...

Abstract Similar to the Bers simultaneous uniformization, product of p -Weil–Petersson Teichmüller spaces for $$p \ge 1$$ p ≥ 1 provides coordinates space embeddings $$\gamma $$ γ real line $${\mathbb {R}}$$ R into comp...

Let X be a Fano manifold of Picard number 1 with numerically effective tangent bundle. According to the principal case of a conjecture of Campana-Peternell’s, X should be biholomorphic to a rational homogeneous manifold G/P , where G is a simple Lie group, and P ⊂ G is a maximal