Szego projections and new invariants for CR and contact manifolds

2006/01/15 by Ponge, Raphael
#53D35 #58J40 #58J42 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Primary 32A25 #Secondary 32V20

paper · doi:10.48550/arxiv.math/0601370

Abstract

In this paper we give a survey of the constructions in math.DG/0510061 of several new invariants for CR and contact manifolds. The latter extend previous constructions of Hirachi and Boutet de Monvel. In addition, we give simple algebro-geometric arguments proving that Hirachi's invariant vanishes on strictly pseudoconvex CR manifolds of dimension 4m+1.

Related

• Contact structures, CR Yamabe invariant, and connected sum
• On contact and finitely Levi-nondegenerate CR algebras
• Szegő kernels and equivariant embedding theorems for CR manifolds
• A CR invariant sphere theorem
• Almost CR manifolds with contracting CR automorphism