Elementary Pseudoconcavity and fields of CR meromorphic functions

TL;DR

This paper introduces the concept of elementary pseudoconcavity for noncompact CR manifolds with the local extension property and generalizes results on algebraic dependence and transcendence degree for CR meromorphic functions.

Contribution

It extends the notion of pseudoconcavity to CR manifolds and generalizes previous results to the noncompact setting.

Findings

Defined elementary pseudoconcavity for CR manifolds.

Generalized algebraic dependence results for CR meromorphic functions.

Extended transcendence degree results to noncompact CR manifolds.

Abstract

Let M be a smooth CR manifold of CR dimension n and CR codimension k, which is not compact, but has the local extension property E. We introduce the notion of "elementary pseudoconcavity" for M, which extends to CR manifolds the concept of a "pseudoconcave" complex manifold. This notion is then used to obtain generalizations, to the noncompact case, of the results of our previous paper about algebraic dependence, transcendence degree and related matters for the field K(M) of CR meromorphic functions on M.